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                           <rdf:li><rdf:Description xmpDM:name="Moving Average (MA) Models Moving Average of order 1: MA(1) b0 is the mean of the time series." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The parameters b0 and b1 cannot be estimated using standard regression formulas since we do not know errors." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The errors depend on the parameters." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="So the only way to find optimal b0 and b1 is by iteration." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Start with some suitable values and change b0 and b1 until SSE is minimized and average of errors is" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="zero." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Consider the data of Example 37.1." xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For this data: We start with b0 = 67.72," xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b1=0.4," xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assuming e0=0, compute all the errors and SSE." xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and SSE = 33542.8" xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="We then adjust a0 and b1 until SSE is minimized and mean error is close to zero." xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp …" xmpDM:startTime="57800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="75100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) The steps are: Starting with and trying various values of b1." xmpDM:startTime="75100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE is minimum at b1=0.475." xmpDM:startTime="75100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE= 33221.06" xmpDM:startTime="75100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="75100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Keeping b1=0.475," xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="try neighboring values of b0 to get average error as close to zero as possible." xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0= 67.475" xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="gives =-0.001" xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE=33221.93" xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="106500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="114933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) The steps are: Starting with and trying various values of b1." xmpDM:startTime="114933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE is minimum at b1=0.475." xmpDM:startTime="114933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE= 33221.06" xmpDM:startTime="114933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="114933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Consider the data of Example 37.1." xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For this data: We start with b0 = 67.72," xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b1=0.4," xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assuming e0=0, compute all the errors and SSE." xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and SSE = 33542.8" xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="We then adjust a0 and b1 until SSE is minimized and mean error is close to zero." xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp …" xmpDM:startTime="116100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="119533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) The steps are: Starting with and trying various values of b1." xmpDM:startTime="119533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE is minimum at b1=0.475." xmpDM:startTime="119533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE= 33221.06" xmpDM:startTime="119533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="119533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Keeping b1=0.475," xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="try neighboring values of b0 to get average error as close to zero as possible." xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0= 67.475" xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="gives =-0.001" xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE=33221.93" xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="120000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models Moving Average of order 1: MA(1) Moving Average of order 2: MA(2) Moving Average of order q: MA(q)" xmpDM:startTime="121100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of order 0: MA(0) (Note: This is also AR(0)) xt-b0 is a white noise." xmpDM:startTime="121100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0 is the mean of the time series." xmpDM:startTime="121100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="121100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Keeping b1=0.475," xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="try neighboring values of b0 to get average error as close to zero as possible." xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0= 67.475" xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="gives =-0.001" xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE=33221.93" xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="122900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models Moving Average of order 1: MA(1) Moving Average of order 2: MA(2) Moving Average of order q: MA(q)" xmpDM:startTime="137967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of order 0: MA(0) (Note: This is also AR(0)) xt-b0 is a white noise." xmpDM:startTime="137967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0 is the mean of the time series." xmpDM:startTime="137967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="137967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="165633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(0) model to the data of Exercise 37.1." xmpDM:startTime="165633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameter b0 and SSE" xmpDM:startTime="165633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models Moving Average of order 1: MA(1) Moving Average of order 2: MA(2) Moving Average of order q: MA(q)" xmpDM:startTime="172633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of order 0: MA(0) (Note: This is also AR(0)) xt-b0 is a white noise." xmpDM:startTime="172633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0 is the mean of the time series." xmpDM:startTime="172633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="172633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="203400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(0) model to the data of Exercise 37.1." xmpDM:startTime="203400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameter b0 and SSE" xmpDM:startTime="203400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models (Cont) Using the backward shift operator B, MA(q): Here, ªq is a polynomial of order q." xmpDM:startTime="211500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="211500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit MA(2) model to the data of Example 37.1" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 1: Setting , we try 9 combinations of b1={0.2,0.3,0.4}" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.2," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.3," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.4}." xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 33490.26" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.4" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2=0.2" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 2: Try 4 new points around the current minimum b0={0.35," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.45}" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.15," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.25}" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32551.62" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.45," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.15" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 3: Try 4 new points around the current minimum." xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.425," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.475}" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.125," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.175}" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32342.61" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.475," xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.125" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="292200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Round 4: Try 4 new points around the current minimum." xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.4625," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.4875}" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.125," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.175}" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32201.58" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.4875," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.125" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 5: Try 4 new points around the current minimum." xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.481," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.493}" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.112," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.137}" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32148.21" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.493," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.137" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Since the decrease in SSN is small (close to 0.1%)," xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="we arbitrarily stop here." xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The model is:" xmpDM:startTime="483500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 38.8" xmpDM:startTime="547200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(1) model to the data of Exercise 37.1." xmpDM:startTime="547200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters b0, b1 and the minimum SSE." xmpDM:startTime="547200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="547200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) For this series, the mean is: The variance is: The autocovariance at lag 1 is: TP_tmp TP_tmp" xmpDM:startTime="573767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="573767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="620600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) For this series, the mean is: The variance is: The autocovariance at lag 1 is: TP_tmp TP_tmp" xmpDM:startTime="631900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="631900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="641167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.9" xmpDM:startTime="677933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the data of Example 37.1:" xmpDM:startTime="677933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelation is zero for all lags k &gt;1." xmpDM:startTime="677933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(1) model is appropriate for this data." xmpDM:startTime="677933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="677933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="690100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) For this series, the mean is: The variance is: The autocovariance at lag 1 is: TP_tmp TP_tmp" xmpDM:startTime="690733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="690733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 38.8" xmpDM:startTime="691367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(1) model to the data of Exercise 37.1." xmpDM:startTime="691367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters b0, b1 and the minimum SSE." xmpDM:startTime="691367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="691367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Round 4: Try 4 new points around the current minimum." xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.4625," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.4875}" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.125," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.175}" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32201.58" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.4875," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.125" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 5: Try 4 new points around the current minimum." xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.481," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.493}" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.112," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.137}" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32148.21" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.493," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.137" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Since the decrease in SSN is small (close to 0.1%)," xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="we arbitrarily stop here." xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The model is:" xmpDM:startTime="691933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit MA(2) model to the data of Example 37.1" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 1: Setting , we try 9 combinations of b1={0.2,0.3,0.4}" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.2," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.3," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.4}." xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 33490.26" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.4" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2=0.2" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 2: Try 4 new points around the current minimum b0={0.35," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.45}" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.15," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.25}" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32551.62" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.45," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.15" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 3: Try 4 new points around the current minimum." xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.425," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.475}" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.125," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.175}" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32342.61" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.475," xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.125" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="692467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models (Cont) Using the backward shift operator B, MA(q): Here, ªq is a polynomial of order q." xmpDM:startTime="692967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="692967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="693500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(0) model to the data of Exercise 37.1." xmpDM:startTime="693500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameter b0 and SSE" xmpDM:startTime="693500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models Moving Average of order 1: MA(1) Moving Average of order 2: MA(2) Moving Average of order q: MA(q)" xmpDM:startTime="694000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of order 0: MA(0) (Note: This is also AR(0)) xt-b0 is a white noise." xmpDM:startTime="694000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0 is the mean of the time series." xmpDM:startTime="694000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="694000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Keeping b1=0.475," xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="try neighboring values of b0 to get average error as close to zero as possible." xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0= 67.475" xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="gives =-0.001" xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE=33221.93" xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="694500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="695000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) The steps are: Starting with and trying various values of b1." xmpDM:startTime="695000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE is minimum at b1=0.475." xmpDM:startTime="695000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE= 33221.06" xmpDM:startTime="695000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="695000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Consider the data of Example 37.1." xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For this data: We start with b0 = 67.72," xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b1=0.4," xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assuming e0=0, compute all the errors and SSE." xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and SSE = 33542.8" xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="We then adjust a0 and b1 until SSE is minimized and mean error is close to zero." xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp …" xmpDM:startTime="695733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average (MA) Models Moving Average of order 1: MA(1) b0 is the mean of the time series." xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The parameters b0 and b1 cannot be estimated using standard regression formulas since we do not know errors." xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The errors depend on the parameters." xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="So the only way to find optimal b0 and b1 is by iteration." xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Start with some suitable values and change b0 and b1 until SSE is minimized and average of errors is" xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="zero." xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp" xmpDM:startTime="696167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.6" xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Using the results of Exercises 37.1," xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="37.4," xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 37.5," xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="determine the partial autocorrelation function at lags 1, 2, 3 for the data of Exercise 37.1." xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine which values are significant." xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Based on this which AR(p) model will be appropriate for this data?" xmpDM:startTime="696700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF (Cont)" xmpDM:startTime="697167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF = Determinant of M" xmpDM:startTime="697900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.6" xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the data of Example 37.1," xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="we have: AR(1): AR(2): Similarly, AR(3): PACF at lags 1, 2, and 3 are: 0.503," xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.180," xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.052" xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(1) is appropriate." xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="698367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining the Order AR(p) ACF of AR(1) is an exponentially decreasing fn of k Fit AR(p) models of order p=0," xmpDM:startTime="698767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1, 2, … Compute the (1-a)% confidence intervals of ap After some p, the last coefficients ap will not be" xmpDM:startTime="698767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="significant for all higher order models." xmpDM:startTime="698767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This highest p is the order of the AR(p) model for the series." xmpDM:startTime="698767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This sequence of last coefficients is also called &quot;Partial Autocorrelation Function (PACF)&quot; Lag k PACF(k) 0 TP_tmp TP_tmp p=8 TP_tmp" xmpDM:startTime="698767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="rk k" xmpDM:startTime="698767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.6" xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the data of Example 37.1," xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="we have: AR(1): AR(2): Similarly, AR(3): PACF at lags 1, 2, and 3 are: 0.503," xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.180," xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.052" xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(1) is appropriate." xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="700100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining the Order AR(p) ACF of AR(1) is an exponentially decreasing fn of k Fit AR(p) models of order p=0," xmpDM:startTime="715700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1, 2, … Compute the (1-a)% confidence intervals of ap After some p, the last coefficients ap will not be" xmpDM:startTime="715700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="significant for all higher order models." xmpDM:startTime="715700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This highest p is the order of the AR(p) model for the series." xmpDM:startTime="715700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This sequence of last coefficients is also called &quot;Partial Autocorrelation Function (PACF)&quot; Lag k PACF(k) 0 TP_tmp TP_tmp p=8 TP_tmp" xmpDM:startTime="715700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="rk k" xmpDM:startTime="715700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.5" xmpDM:startTime="716167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an AR(3) model to the data of Exercise 37.1." xmpDM:startTime="716167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters a0, a1, a2, a3 and the SSE using multiple regression." xmpDM:startTime="716167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="716167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.4" xmpDM:startTime="716700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an AR(2) model to the data of Exercise 37.1." xmpDM:startTime="716700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters a0, a1, a2 and the SSE using multiple regression." xmpDM:startTime="716700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Repeat the determination of parameters using autocorrelation function values." xmpDM:startTime="716700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="716700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.5" xmpDM:startTime="717200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Consider the data of Example 37.1" xmpDM:startTime="717200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and fit an AR(2) model: SSE= 31979.39" xmpDM:startTime="717200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Small sample  Values of a0, a1, and a2 are approximate." xmpDM:startTime="717200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exact model by regression: SSE=31969.99" xmpDM:startTime="717200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="717200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont) All sums are from t=p to t=n and have n-p terms." xmpDM:startTime="717633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For larger data sets: rk is the autocorrelation at lag k (i,j)th term = r|i-j|" xmpDM:startTime="717633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont) The equations can be written as: Note: All sums are for t=3 to n." xmpDM:startTime="718200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="n-2 terms." xmpDM:startTime="718200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Multiplying by the inverse of the first matrix, we get: TP_tmp TP_tmp" xmpDM:startTime="718200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation The coefficients ai's can be estimated by minimizing SSE using Multiple Linear Regression." xmpDM:startTime="718600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Optimal a0, a1, and a2  Minimize SSE Set the first differential to zero: TP_tmp TP_tmp TP_tmp" xmpDM:startTime="718600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Similarly, Or Using this notation, AR(p) model is: Here, Áp is a polynomial of degree p." xmpDM:startTime="719133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp Backward Shift Operator TP_tmp TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="719133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Model xt is a function of the last p values: AR(2): AR(3): TP_tmp TP_tmp TP_tmp" xmpDM:startTime="719633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.3" xmpDM:startTime="720133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Conduct visual tests to verify whether or not the AR(1) model fitted in Exercise 37.1" xmpDM:startTime="720133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is appropriate ." xmpDM:startTime="720133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="720133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont) et TP_tmp e z -80 -60 -40 -20 0 20 40 60 80 -3 -2 -1 0" xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1 2 3 et t 3." xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Errors et vs." xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="predicted values 4." xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q-Q Plot of errors 5." xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Errors et vs." xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t" xmpDM:startTime="720667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont) 2." xmpDM:startTime="721467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Plot of xt vs." xmpDM:startTime="721467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xt-1 xt-1 xt" xmpDM:startTime="721467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests for AR(1) Models Plot xt as a function of t and look for trends xt vs." xmpDM:startTime="722033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xt-1 for linearity Errors et vs." xmpDM:startTime="722033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="predicted values for additivity Q-Q Plot of errors for Normality Errors et vs." xmpDM:startTime="722033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t for IID TP_tmp 1." xmpDM:startTime="722033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Plot of xt" xmpDM:startTime="722033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assumptions for AR(1) Models xt is a Stationary process Linear relationship between successive values Normal Independent identically distributed errors: Normal" xmpDM:startTime="722500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="errors Independent errors Additive errors" xmpDM:startTime="722500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.2" xmpDM:startTime="723033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine autocorrelations at lag 0 through 2 for the data of Exercise 37.1" xmpDM:startTime="723033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and determine which of these autocorrelations are significant at 95% confidence." xmpDM:startTime="723033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="723033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.3" xmpDM:startTime="723567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the data of Example 37.1:" xmpDM:startTime="723567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="n=50 TP_tmp r2 is not significantly different from zero." xmpDM:startTime="723567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="723567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.2" xmpDM:startTime="825100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine autocorrelations at lag 0 through 2 for the data of Exercise 37.1" xmpDM:startTime="825100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and determine which of these autocorrelations are significant at 95% confidence." xmpDM:startTime="825100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="825100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assumptions for AR(1) Models xt is a Stationary process Linear relationship between successive values Normal Independent identically distributed errors: Normal" xmpDM:startTime="825267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="errors Independent errors Additive errors" xmpDM:startTime="825267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests for AR(1) Models Plot xt as a function of t and look for trends xt vs." xmpDM:startTime="825400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xt-1 for linearity Errors et vs." xmpDM:startTime="825400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="predicted values for additivity Q-Q Plot of errors for Normality Errors et vs." xmpDM:startTime="825400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t for IID TP_tmp 1." xmpDM:startTime="825400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Plot of xt" xmpDM:startTime="825400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont) 2." xmpDM:startTime="825567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Plot of xt vs." xmpDM:startTime="825567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xt-1 xt-1 xt" xmpDM:startTime="825567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont) et TP_tmp e z -80 -60 -40 -20 0 20 40 60 80 -3 -2 -1 0" xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1 2 3 et t 3." xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Errors et vs." xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="predicted values 4." xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q-Q Plot of errors 5." xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Errors et vs." xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t" xmpDM:startTime="825733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.3" xmpDM:startTime="825867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Conduct visual tests to verify whether or not the AR(1) model fitted in Exercise 37.1" xmpDM:startTime="825867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is appropriate ." xmpDM:startTime="825867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="825867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Model xt is a function of the last p values: AR(2): AR(3): TP_tmp TP_tmp TP_tmp" xmpDM:startTime="826033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Similarly, Or Using this notation, AR(p) model is: Here, Áp is a polynomial of degree p." xmpDM:startTime="826200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp Backward Shift Operator TP_tmp TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="826200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation The coefficients ai's can be estimated by minimizing SSE using Multiple Linear Regression." xmpDM:startTime="826367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Optimal a0, a1, and a2  Minimize SSE Set the first differential to zero: TP_tmp TP_tmp TP_tmp" xmpDM:startTime="826367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont) The equations can be written as: Note: All sums are for t=3 to n." xmpDM:startTime="826500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="n-2 terms." xmpDM:startTime="826500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Multiplying by the inverse of the first matrix, we get: TP_tmp TP_tmp" xmpDM:startTime="826500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont) All sums are from t=p to t=n and have n-p terms." xmpDM:startTime="826700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For larger data sets: rk is the autocorrelation at lag k (i,j)th term = r|i-j|" xmpDM:startTime="826700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.5" xmpDM:startTime="826867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Consider the data of Example 37.1" xmpDM:startTime="826867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and fit an AR(2) model: SSE= 31979.39" xmpDM:startTime="826867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Small sample  Values of a0, a1, and a2 are approximate." xmpDM:startTime="826867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exact model by regression: SSE=31969.99" xmpDM:startTime="826867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="826867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.4" xmpDM:startTime="827033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an AR(2) model to the data of Exercise 37.1." xmpDM:startTime="827033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters a0, a1, a2 and the SSE using multiple regression." xmpDM:startTime="827033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Repeat the determination of parameters using autocorrelation function values." xmpDM:startTime="827033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="827033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.5" xmpDM:startTime="827233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an AR(3) model to the data of Exercise 37.1." xmpDM:startTime="827233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters a0, a1, a2, a3 and the SSE using multiple regression." xmpDM:startTime="827233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="827233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining the Order AR(p) ACF of AR(1) is an exponentially decreasing fn of k Fit AR(p) models of order p=0," xmpDM:startTime="827400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1, 2, … Compute the (1-a)% confidence intervals of ap After some p, the last coefficients ap will not be" xmpDM:startTime="827400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="significant for all higher order models." xmpDM:startTime="827400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This highest p is the order of the AR(p) model for the series." xmpDM:startTime="827400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This sequence of last coefficients is also called &quot;Partial Autocorrelation Function (PACF)&quot; Lag k PACF(k) 0 TP_tmp TP_tmp p=8 TP_tmp" xmpDM:startTime="827400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="rk k" xmpDM:startTime="827400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.6" xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the data of Example 37.1," xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="we have: AR(1): AR(2): Similarly, AR(3): PACF at lags 1, 2, and 3 are: 0.503," xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.180," xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.052" xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(1) is appropriate." xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="827600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF = Determinant of M" xmpDM:startTime="827833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF (Cont)" xmpDM:startTime="828267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.6" xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Using the results of Exercises 37.1," xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="37.4," xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 37.5," xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="determine the partial autocorrelation function at lags 1, 2, 3 for the data of Exercise 37.1." xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine which values are significant." xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Based on this which AR(p) model will be appropriate for this data?" xmpDM:startTime="828500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average (MA) Models Moving Average of order 1: MA(1) b0 is the mean of the time series." xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The parameters b0 and b1 cannot be estimated using standard regression formulas since we do not know errors." xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The errors depend on the parameters." xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="So the only way to find optimal b0 and b1 is by iteration." xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Start with some suitable values and change b0 and b1 until SSE is minimized and average of errors is" xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="zero." xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp" xmpDM:startTime="828733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Consider the data of Example 37.1." xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For this data: We start with b0 = 67.72," xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b1=0.4," xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assuming e0=0, compute all the errors and SSE." xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and SSE = 33542.8" xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="We then adjust a0 and b1 until SSE is minimized and mean error is close to zero." xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp …" xmpDM:startTime="829000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="829533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) The steps are: Starting with and trying various values of b1." xmpDM:startTime="829533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE is minimum at b1=0.475." xmpDM:startTime="829533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE= 33221.06" xmpDM:startTime="829533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="829533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Keeping b1=0.475," xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="try neighboring values of b0 to get average error as close to zero as possible." xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0= 67.475" xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="gives =-0.001" xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="SSE=33221.93" xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="830067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models Moving Average of order 1: MA(1) Moving Average of order 2: MA(2) Moving Average of order q: MA(q)" xmpDM:startTime="830367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Moving Average of order 0: MA(0) (Note: This is also AR(0)) xt-b0 is a white noise." xmpDM:startTime="830367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b0 is the mean of the time series." xmpDM:startTime="830367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="830367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="831800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(0) model to the data of Exercise 37.1." xmpDM:startTime="831800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameter b0 and SSE" xmpDM:startTime="831800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models (Cont) Using the backward shift operator B, MA(q): Here, ªq is a polynomial of order q." xmpDM:startTime="833367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="833367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit MA(2) model to the data of Example 37.1" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 1: Setting , we try 9 combinations of b1={0.2,0.3,0.4}" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.2," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.3," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.4}." xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 33490.26" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.4" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2=0.2" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 2: Try 4 new points around the current minimum b0={0.35," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.45}" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.15," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.25}" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32551.62" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.45," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.15" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 3: Try 4 new points around the current minimum." xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.425," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.475}" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.125," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.175}" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32342.61" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.475," xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.125" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="833800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(Cont) Round 4: Try 4 new points around the current minimum." xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.4625," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.4875}" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.125," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.175}" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32201.58" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.4875," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.125" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Round 5: Try 4 new points around the current minimum." xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Try b1={0.481," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.493}" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and b2={0.112," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.137}" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Minimum SSE is 32148.21" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="at b1=0.493," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="b2=0.137" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Since the decrease in SSN is small (close to 0.1%)," xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="we arbitrarily stop here." xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The model is:" xmpDM:startTime="834300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 38.8" xmpDM:startTime="835333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(1) model to the data of Exercise 37.1." xmpDM:startTime="835333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters b0, b1 and the minimum SSE." xmpDM:startTime="835333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="835333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) For this series, the mean is: The variance is: The autocovariance at lag 1 is: TP_tmp TP_tmp" xmpDM:startTime="837600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="837600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="838267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.9" xmpDM:startTime="838700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the data of Example 37.1:" xmpDM:startTime="838700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelation is zero for all lags k &gt;1." xmpDM:startTime="838700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(1) model is appropriate for this data." xmpDM:startTime="838700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="838700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.10" xmpDM:startTime="841267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The order of the last significant rk determines the order of the MA(q) model." xmpDM:startTime="841267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For the following data, all autocorrelations at lag 9 and higher are zero  MA(8) model would be appropriate Lag" xmpDM:startTime="841267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="k Autocorrelation rk 0 TP_tmp TP_tmp q=8" xmpDM:startTime="841267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.9" xmpDM:startTime="879167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fit an MA(2) model to the data of Exercise 37.2." xmpDM:startTime="879167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine parameters b0, b1, b2 and the minimum SSE." xmpDM:startTime="879167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For this data, which model would you choose MA(0), MA(1) or MA(2) and why?" xmpDM:startTime="879167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Duality of AR(p) vs." xmpDM:startTime="925233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Determining the coefficients of AR(p) is straight forward but determining the order p requires an iterative procedure Determining the" xmpDM:startTime="925233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="order q of MA(q) is straight forward but determining the coefficients requires an iterative procedure" xmpDM:startTime="925233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Non-Stationarity: Integrated Models In the white noise model MA(0): The mean b0 is independent of time." xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If it appears that the time series in increasing approximately linearly with time, the first difference of the series can" xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="be modeled as white noise: Or using the B operator: (1-B)xt = xt-xt-1 This is called an &quot;integrated&quot; model of" xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="order 1 or I(1)." xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Since the errors are integrated to obtain x." xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Note that xt is not stationary but (1-B)xt is stationary." xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="t xt t (1-B)xt" xmpDM:startTime="999267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Integrated Models (Cont) If the time series is parabolic, the second difference can be modeled as white noise: Or This" xmpDM:startTime="1205667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is an I(2) model." xmpDM:startTime="1205667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Also written as: Where Operator D = 1-B t xt" xmpDM:startTime="1205667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ARMA and ARIMA Models It is possible to combine AR, MA, and I models ARMA(p, q) Model: ARIMA(p,d,q) Model: Using" xmpDM:startTime="1287667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="algebraic manipulations, it is possible to transform AR models to MA models and vice versa." xmpDM:startTime="1287667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp" xmpDM:startTime="1287667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1508400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 39.10" xmpDM:startTime="1660400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Convert the following AR(1) model to an equivalent MA model:" xmpDM:startTime="1660400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Non-Stationarity due to Seasonality The mean temperature in December is always lower than that in November and in May it" xmpDM:startTime="1669333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="always higher than that in March Temperature has a yearly season." xmpDM:startTime="1669333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="One possible model could be I(12): or" xmpDM:startTime="1669333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1795800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.11" xmpDM:startTime="2096200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Write the expression for SARIMA(1,0,1)(0,1,0)12 model in terms of x’s and e’s." xmpDM:startTime="2096200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2096200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Observation: Every 16th frame is a large (I) frame." xmpDM:startTime="2098567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 37.1:" xmpDM:startTime="2098567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mobile Video" xmpDM:startTime="2098567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.11" xmpDM:startTime="2099500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Write the expression for SARIMA(1,0,1)(0,1,0)12 model in terms of x’s and e’s." xmpDM:startTime="2099500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2099500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Observation: Every 16th frame is a large (I) frame." xmpDM:startTime="2111833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 37.1:" xmpDM:startTime="2111833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mobile Video" xmpDM:startTime="2111833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="A closer look at the ACF graph shows a strong continual correlation every 16 lag  GOP size Traffic Modeling" xmpDM:startTime="2298500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="– All Frames Result: SARIMA (1, 0, 1)x(1,1,1)s Model, s=group size =16" xmpDM:startTime="2298500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Observation: Every 16th frame is a large (I) frame." xmpDM:startTime="2367167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 37.1:" xmpDM:startTime="2367167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mobile Video" xmpDM:startTime="2367167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="A closer look at the ACF graph shows a strong continual correlation every 16 lag  GOP size Traffic Modeling" xmpDM:startTime="2374733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="– All Frames Result: SARIMA (1, 0, 1)x(1,1,1)s Model, s=group size =16" xmpDM:startTime="2374733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Validation" xmpDM:startTime="2431100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary AR(1) Model: MA(1) Model: ARIMA(1,1,1) Model: Seasonal ARIMA (1,0,1)x(0,1,0)12 model: TP_tmp TP_tmp TP_tmp" xmpDM:startTime="2467733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Scan This to Download These Slides thankyou Raj Jain http://rajjain.com" xmpDM:startTime="2531800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2531800" xmpDM:duration="1000"/></rdf:li></rdf:Seq>
                     </xmpDM:markers>
                  </rdf:Description>
               </rdf:li>
               <rdf:li>
                  <rdf:Description xmpDM:trackType="TableOfContents" xmpDM:frameRate="f1000" xmpDM:trackName="Table of Contents">
                     <xmpDM:markers>
                        <rdf:Seq>
                           <rdf:li><rdf:Description xmpDM:name="       Moving Average (MA) Models" xmpDM:startTime="0" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="0" tscDM:imageoffset="0" tscDM:imagerect="0, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="57800" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="1" tscDM:imageoffset="0" tscDM:imagerect="75, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="75100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="2" tscDM:imageoffset="0" tscDM:imagerect="150, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="106500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="3" tscDM:imageoffset="0" tscDM:imagerect="225, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="114933" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="4" tscDM:imageoffset="0" tscDM:imagerect="300, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="116100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="5" tscDM:imageoffset="0" tscDM:imagerect="375, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="119533" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="6" tscDM:imageoffset="0" tscDM:imagerect="450, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="120000" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="7" tscDM:imageoffset="0" tscDM:imagerect="525, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models" xmpDM:startTime="121100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="8" tscDM:imageoffset="0" tscDM:imagerect="600, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="122900" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="9" tscDM:imageoffset="0" tscDM:imagerect="675, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models" xmpDM:startTime="137967" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="10" tscDM:imageoffset="0" tscDM:imagerect="750, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="165633" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="11" tscDM:imageoffset="0" tscDM:imagerect="825, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models" xmpDM:startTime="172633" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="12" tscDM:imageoffset="0" tscDM:imagerect="900, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="203400" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="13" tscDM:imageoffset="0" tscDM:imagerect="975, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models (Cont)" xmpDM:startTime="211500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="14" tscDM:imageoffset="0" tscDM:imagerect="1050, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="292200" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="15" tscDM:imageoffset="0" tscDM:imagerect="1125, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8 (Cont)" xmpDM:startTime="483500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="16" tscDM:imageoffset="0" tscDM:imagerect="1200, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 38.8" xmpDM:startTime="547200" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="17" tscDM:imageoffset="0" tscDM:imagerect="1275, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1)" xmpDM:startTime="573767" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="18" tscDM:imageoffset="0" tscDM:imagerect="1350, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) (Cont)" xmpDM:startTime="620600" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="19" tscDM:imageoffset="0" tscDM:imagerect="1425, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1)" xmpDM:startTime="631900" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="20" tscDM:imageoffset="0" tscDM:imagerect="1500, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) (Cont)" xmpDM:startTime="641167" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="21" tscDM:imageoffset="0" tscDM:imagerect="1575, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.9" xmpDM:startTime="677933" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="22" tscDM:imageoffset="0" tscDM:imagerect="1650, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) (Cont)" xmpDM:startTime="690100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="23" tscDM:imageoffset="0" tscDM:imagerect="1725, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1)" xmpDM:startTime="690733" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="24" tscDM:imageoffset="0" tscDM:imagerect="1800, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 38.8" xmpDM:startTime="691367" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="25" tscDM:imageoffset="0" tscDM:imagerect="1875, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8 (Cont)" xmpDM:startTime="691933" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="26" tscDM:imageoffset="0" tscDM:imagerect="1950, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="692467" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="27" tscDM:imageoffset="0" tscDM:imagerect="2025, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models (Cont)" xmpDM:startTime="692967" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="28" tscDM:imageoffset="0" tscDM:imagerect="2100, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="693500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="29" tscDM:imageoffset="0" tscDM:imagerect="2175, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models" xmpDM:startTime="694000" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="30" tscDM:imageoffset="0" tscDM:imagerect="2250, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="694500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="31" tscDM:imageoffset="0" tscDM:imagerect="2325, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="695000" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="32" tscDM:imageoffset="0" tscDM:imagerect="2400, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="695733" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="33" tscDM:imageoffset="0" tscDM:imagerect="2475, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="       Moving Average (MA) Models" xmpDM:startTime="696167" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="34" tscDM:imageoffset="0" tscDM:imagerect="2550, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.6" xmpDM:startTime="696700" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="35" tscDM:imageoffset="0" tscDM:imagerect="2625, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF (Cont)" xmpDM:startTime="697167" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="36" tscDM:imageoffset="0" tscDM:imagerect="2700, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF" xmpDM:startTime="697900" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="37" tscDM:imageoffset="0" tscDM:imagerect="2775, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.6" xmpDM:startTime="698367" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="38" tscDM:imageoffset="0" tscDM:imagerect="2850, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="        Determining the Order AR(p)" xmpDM:startTime="698767" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="39" tscDM:imageoffset="0" tscDM:imagerect="2925, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.6" xmpDM:startTime="700100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="40" tscDM:imageoffset="0" tscDM:imagerect="3000, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="        Determining the Order AR(p)" xmpDM:startTime="715700" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="41" tscDM:imageoffset="0" tscDM:imagerect="3075, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.5" xmpDM:startTime="716167" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="42" tscDM:imageoffset="0" tscDM:imagerect="3150, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.4" xmpDM:startTime="716700" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="43" tscDM:imageoffset="0" tscDM:imagerect="3225, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.5" xmpDM:startTime="717200" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="44" tscDM:imageoffset="0" tscDM:imagerect="3300, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont)" xmpDM:startTime="717633" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="45" tscDM:imageoffset="0" tscDM:imagerect="3375, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont)" xmpDM:startTime="718200" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="46" tscDM:imageoffset="0" tscDM:imagerect="3450, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="          AR(p) Parameter Estimation" xmpDM:startTime="718600" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="47" tscDM:imageoffset="0" tscDM:imagerect="3525, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Backward Shift Operator" xmpDM:startTime="719133" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="48" tscDM:imageoffset="0" tscDM:imagerect="3600, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Model" xmpDM:startTime="719633" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="49" tscDM:imageoffset="0" tscDM:imagerect="3675, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.3" xmpDM:startTime="720133" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="50" tscDM:imageoffset="0" tscDM:imagerect="3750, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont)" xmpDM:startTime="720667" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="51" tscDM:imageoffset="0" tscDM:imagerect="3825, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont)" xmpDM:startTime="721467" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="52" tscDM:imageoffset="0" tscDM:imagerect="3900, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests for AR(1) Models" xmpDM:startTime="722033" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="53" tscDM:imageoffset="0" tscDM:imagerect="3975, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assumptions for AR(1) Models" xmpDM:startTime="722500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="54" tscDM:imageoffset="0" tscDM:imagerect="50, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.2" xmpDM:startTime="723033" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="55" tscDM:imageoffset="0" tscDM:imagerect="125, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.3" xmpDM:startTime="723567" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="56" tscDM:imageoffset="0" tscDM:imagerect="200, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.2" xmpDM:startTime="825100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="57" tscDM:imageoffset="0" tscDM:imagerect="275, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Assumptions for AR(1) Models" xmpDM:startTime="825267" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="58" tscDM:imageoffset="0" tscDM:imagerect="350, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests for AR(1) Models" xmpDM:startTime="825400" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="59" tscDM:imageoffset="0" tscDM:imagerect="425, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont)" xmpDM:startTime="825567" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="60" tscDM:imageoffset="0" tscDM:imagerect="500, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Visual Tests (Cont)" xmpDM:startTime="825733" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="61" tscDM:imageoffset="0" tscDM:imagerect="575, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.3" xmpDM:startTime="825867" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="62" tscDM:imageoffset="0" tscDM:imagerect="650, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Model" xmpDM:startTime="826033" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="63" tscDM:imageoffset="0" tscDM:imagerect="725, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Backward Shift Operator" xmpDM:startTime="826200" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="64" tscDM:imageoffset="0" tscDM:imagerect="800, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="          AR(p) Parameter Estimation" xmpDM:startTime="826367" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="65" tscDM:imageoffset="0" tscDM:imagerect="875, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont)" xmpDM:startTime="826500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="66" tscDM:imageoffset="0" tscDM:imagerect="950, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="AR(p) Parameter Estimation (Cont)" xmpDM:startTime="826700" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="67" tscDM:imageoffset="0" tscDM:imagerect="1025, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.5" xmpDM:startTime="826867" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="68" tscDM:imageoffset="0" tscDM:imagerect="1100, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.4" xmpDM:startTime="827033" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="69" tscDM:imageoffset="0" tscDM:imagerect="1175, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.5" xmpDM:startTime="827233" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="70" tscDM:imageoffset="0" tscDM:imagerect="1250, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="        Determining the Order AR(p)" xmpDM:startTime="827400" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="71" tscDM:imageoffset="0" tscDM:imagerect="1325, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.6" xmpDM:startTime="827600" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="72" tscDM:imageoffset="0" tscDM:imagerect="1400, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF" xmpDM:startTime="827833" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="73" tscDM:imageoffset="0" tscDM:imagerect="1475, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Computing PACF (Cont)" xmpDM:startTime="828267" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="74" tscDM:imageoffset="0" tscDM:imagerect="1550, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.6" xmpDM:startTime="828500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="75" tscDM:imageoffset="0" tscDM:imagerect="1625, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="       Moving Average (MA) Models" xmpDM:startTime="828733" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="76" tscDM:imageoffset="0" tscDM:imagerect="1700, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4" xmpDM:startTime="829000" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="77" tscDM:imageoffset="0" tscDM:imagerect="1775, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="829533" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="78" tscDM:imageoffset="0" tscDM:imagerect="1850, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.4 (Cont)" xmpDM:startTime="830067" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="79" tscDM:imageoffset="0" tscDM:imagerect="1925, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models" xmpDM:startTime="830367" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="80" tscDM:imageoffset="0" tscDM:imagerect="2000, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.7" xmpDM:startTime="831800" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="81" tscDM:imageoffset="0" tscDM:imagerect="2075, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="MA(q) Models (Cont)" xmpDM:startTime="833367" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="82" tscDM:imageoffset="0" tscDM:imagerect="2150, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8" xmpDM:startTime="833800" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="83" tscDM:imageoffset="0" tscDM:imagerect="2225, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.8 (Cont)" xmpDM:startTime="834300" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="84" tscDM:imageoffset="0" tscDM:imagerect="2300, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 38.8" xmpDM:startTime="835333" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="85" tscDM:imageoffset="0" tscDM:imagerect="2375, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1)" xmpDM:startTime="837600" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="86" tscDM:imageoffset="0" tscDM:imagerect="2450, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Autocorrelations for MA(1) (Cont)" xmpDM:startTime="838267" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="87" tscDM:imageoffset="0" tscDM:imagerect="2525, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.9" xmpDM:startTime="838700" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="88" tscDM:imageoffset="0" tscDM:imagerect="2600, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="       Example 37.10" xmpDM:startTime="841267" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="89" tscDM:imageoffset="0" tscDM:imagerect="2675, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.9" xmpDM:startTime="879167" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="90" tscDM:imageoffset="0" tscDM:imagerect="2750, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Duality of AR(p) vs. MA(q)" xmpDM:startTime="925233" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="91" tscDM:imageoffset="0" tscDM:imagerect="2825, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Non-Stationarity: Integrated Models" xmpDM:startTime="999267" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="92" tscDM:imageoffset="0" tscDM:imagerect="2900, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Integrated Models (Cont)" xmpDM:startTime="1205667" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="93" tscDM:imageoffset="0" tscDM:imagerect="2975, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ARMA and ARIMA Models" xmpDM:startTime="1287667" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="94" tscDM:imageoffset="0" tscDM:imagerect="3050, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example 37.11" xmpDM:startTime="1508400" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="95" tscDM:imageoffset="0" tscDM:imagerect="3125, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 39.10" xmpDM:startTime="1660400" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="96" tscDM:imageoffset="0" tscDM:imagerect="3200, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Non-Stationarity due to Seasonality" xmpDM:startTime="1669333" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="97" tscDM:imageoffset="0" tscDM:imagerect="3275, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Seasonal ARIMA (SARIMA) Models" xmpDM:startTime="1795800" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="98" tscDM:imageoffset="0" tscDM:imagerect="3350, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.11" xmpDM:startTime="2096200" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="99" tscDM:imageoffset="0" tscDM:imagerect="3425, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 37.1: Mobile Video" xmpDM:startTime="2098567" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="100" tscDM:imageoffset="0" tscDM:imagerect="3500, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Exercise 37.11" xmpDM:startTime="2099500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="101" tscDM:imageoffset="0" tscDM:imagerect="3575, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 37.1: Mobile Video" xmpDM:startTime="2111833" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="102" tscDM:imageoffset="0" tscDM:imagerect="3650, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="       Traffic Modeling – All Frames" xmpDM:startTime="2298500" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="103" tscDM:imageoffset="0" tscDM:imagerect="3725, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Case Study 37.1: Mobile Video" xmpDM:startTime="2367167" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="104" tscDM:imageoffset="0" tscDM:imagerect="3800, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="       Traffic Modeling – All Frames" xmpDM:startTime="2374733" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="105" tscDM:imageoffset="0" tscDM:imagerect="3875, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Validation" xmpDM:startTime="2431100" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="106" tscDM:imageoffset="0" tscDM:imagerect="3950, 56, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary" xmpDM:startTime="2467733" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="107" tscDM:imageoffset="0" tscDM:imagerect="25, 112, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Scan This to Download These Slides" xmpDM:startTime="2531800" tscDM:image="k_37tsa2_Thumbnails.png" tscDM:imageindex="108" tscDM:imageoffset="0" tscDM:imagerect="100, 112, 75, 56"/></rdf:li></rdf:Seq>
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         <tscDM:controller>
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                  <rdf:Bag>
                     <rdf:li xmpDM:name="autohide" xmpDM:value="true"/><rdf:li xmpDM:name="autoplay" xmpDM:value="false"/><rdf:li xmpDM:name="loop" xmpDM:value="false"/><rdf:li xmpDM:name="searchable" xmpDM:value="true"/><rdf:li xmpDM:name="captionsenabled" xmpDM:value="false"/><rdf:li xmpDM:name="sidebarenabled" xmpDM:value="false"/><rdf:li xmpDM:name="unicodeenabled" xmpDM:value="false"/><rdf:li xmpDM:name="backgroundcolor" xmpDM:value="000000"/><rdf:li xmpDM:name="sidebarlocation" xmpDM:value="left"/><rdf:li xmpDM:name="endaction" xmpDM:value="stop"/><rdf:li xmpDM:name="endactionparam" xmpDM:value="true"/><rdf:li xmpDM:name="locale" xmpDM:value="en-US"/></rdf:Bag>
               </tscDM:parameters>
               <tscDM:controllerText>
                  <rdf:Bag>
                  </rdf:Bag>
               </tscDM:controllerText>
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         </tscDM:controller>
         <tscDM:contentList>
            <rdf:Description>
               <tscDM:files>
                  <rdf:Seq>
                     <rdf:li xmpDM:name="0" xmpDM:value="k_37tsa2.mp4"/><rdf:li xmpDM:name="1" xmpDM:value="k_37tsa2_First_Frame.png"/><rdf:li xmpDM:name="2" xmpDM:value="k_37tsa2_Thumbnails.png"/></rdf:Seq>
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         </tscDM:contentList>
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</x:xmpmeta>