tailieunhanh - SAS/ETS 9.22 User's Guide 34

SAS/Ets User's Guide 34. 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 | 322 F Chapter 8 The AUTOREG Procedure Figure Autocorrelated Time Series Note that when the series is above or below the OLS regression trend line it tends to remain above below the trend for several periods. This pattern is an example of positive autocorrelation. Time series regression usually involves independent variables other than a time trend. However the simple time trend model is convenient for illustrating regression with autocorrelated errors and the series Y shown in Figure is used in the following introductory examples. Ordinary Least Squares Regression To use the AUTOREG procedure specify the input data set in the PROC AUTOREG statement and specify the regression model in a MODEL statement. Specify the model by first naming the dependent variable and then listing the regressors after an equal sign as is done in other SAS regression procedures. The following statements regress Y on TIME by using ordinary least squares proc autoreg data a model y time run The AUTOREG procedure output is shown in Figure . Regression with Autocorrelated Errors F 323 Figure PROC AUTOREG Results for OLS Estimation Autocorrelated Time Series SSE The AUTOREG Procedure Dependent Variable y Ordinary Least Squares Estimates DFE 34 MSE Root MSE SBC AIC MAE AICC MAPE HQC Durbin- Watson Regress R-Square Variable Total R-Square Parameter Estimates Standard Approx DF Estimate Error t Value Pr t Intercept 1 .0001 time 1 .0001 The output first shows statistics for the model residuals. The model root mean square error Root MSE is and the model R2 is . Notice that two R2 statistics are shown one for the regression model Reg Rsq and one for the full model Total Rsq that includes the autoregressive error process if any. In this case an autoregressive error model is not used so the two R2 statistics are the same. Other