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Unformatted text preview: Chapter 21 Time Series Models There are no exercises or applications in Chapter 21. 131 Chapter 22 Nonstationary Data Exercise 1. The autocorrelations are simple to obtain just by multiplying out v t 2 , v t v t1 and so on. The autocovariances are 1+ 1 2 + 2 2 ,  2 (1  2 ),  2 , 0, 0, 0... which provides the autocorrelations by division by the first of these. The partial autocorrelations are messy, and can be obtained by the Yule Walker equations. Alternatively (and much more simply), we can make use of the observation in Section 21.2.3 that the partial autocorrelations for the MA(2) process mirror tha autocorrelations for an AR(2). Thus, the results in Section 21.2.3 for the AR(2) can be used directly. Applications 1. ADF Test ++  Ordinary least squares regression Weighting variable = none   Dep. var. = R Mean= 8.212678571 , S.D.= .7762719558   Model size: Observations = 56, Parameters = 6, Deg.Fr.= 50   Residuals: Sum of squares= .9651001703 , Std.Dev.= .13893   Fit: Rsquared= .970881, Adjusted Rsquared = .96797   Model test: F[ 5, 50] = 333.41, Prob value = .00000   Diagnostic: LogL = 34.2439, Restricted(b=0) LogL = 64.7739   LogAmemiyaPrCrt.= 3.846, Akaike Info. Crt.= 1.009   Autocorrel: DurbinWatson Statistic = 1.91589, Rho = .04205  ++ +++++++ Variable  Coefficient  Standard Error tratio P[T>t]  Mean of X +++++++ Constant .2565690959 .47172815 .544 .5889 T .4401352136E03 .25092142E02 .175 .8615 32.500000 R1 .9653227410 .48183346E01 20.034 .0000 8.2305357 DR1 .5600009441 .14342088 3.905 .0003 .12321429E01 DR2 .1739775168 .14781417 1.177 .2448 .20535714E01 DR3 .7792177815E03 .11072916 .007 .9944 .11607143E01 (Note: E+nn or Enn means multiply by 10 to + or nn power.) (Note: E+nn or Enn means multiply by 10 to + or nn power....
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This note was uploaded on 11/13/2011 for the course ECE 4105 taught by Professor Dr.fang during the Spring '10 term at University of Florida.
 Spring '10
 Dr.Fang

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