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SAS/ETS 9.22 User's Guide 35

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SAS/Ets 9.22 User's Guide 35. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 332 F Chapter 8 The AUTOREG Procedure Figure 8.8 continued Parameter Estimates Variable DF Estimate Standard Error t Value Approx Pr t Intercept 1 1.5742 0.9300 1.69 0.0999 ylag 1 0.9376 0.0510 18.37 .0001 Stepwise Autoregression Once you determine that autocorrelation correction is needed you must select the order of the autoregressive error model to use. One way to select the order of the autoregressive error model is stepwise autoregression. The stepwise autoregression method initially fits a high-order model with many autoregressive lags and then sequentially removes autoregressive parameters until all remaining autoregressive parameters have significant t tests. To use stepwise autoregression specify the BACKSTEP option and specify a large order with the NLAG option. The following statements show the stepwise feature using an initial order of 5 stepwise autoregression proc autoreg data a model y time method ml nlag 5 backstep run The results are shown in Figure 8.9. Figure 8.9 Stepwise Autoregression Forecasting Autocorrelated Time Series SSE The AUTOREG Procedure Dependent Variable y Ordinary Least Squares Estimates 214.953429 DFE 34 MSE 6.32216 Root MSE 2.51439 SBC 173.659101 AIC 170.492063 MAE 2.01903356 AICC 170.855699 MAPE 12.5270666 HQC 171.597444 Durbin- -Watson 0.4752 Regress R-Square 0.8200 Total R-Square 0.8200 Stepwise Autoregression F 333 Figure 8.9 continued Parameter Estimates Standard Approx Variable DF Estimate Error t Value Pr t Intercept 1 8.2308 0.8559 9.62 .0001 time 1 0.5021 0.0403 12.45 .0001 Estimates of Autocorrelations Lag Covariance Correlation -198765432101234567891 0 5.9709 1.000000 1 4.5169 0.756485 2 2.0241 0.338995 3 -0.4402 -0.073725 4 -2.1175 -0.354632 5 -2.8534 -0.477887 Backward Elimination of Autoregressive Terms Lag Estimate t Value Pr t 4 -0.052908 -0.20 0.8442 3 0.115986 0.57 0.5698 5 0.131734 1.21 0.2340 The estimates of the autocorrelations are shown for 5 lags. The backward elimination of autoregressive terms report .