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SAS/ETS 9.22 User's Guide 22

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SAS/Ets 9.22 User's Guide 22. 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 | 202 F Chapter 7 The ARIMA Procedure Figure 7.8 Parameter Estimates for AR 1 Model The ARIMA Procedure Conditional Least Squares Estimation Standard Approx Parameter Estimate Error t Value Pr t Lag MU 0.90280 0.65984 1.37 0.1744 0 AR1 1 0.86847 0.05485 15.83 .0001 1 The table of parameter estimates is titled Conditional Least Squares Estimation which indicates the estimation method used. You can request different estimation methods with the METHOD option. The table of parameter estimates lists the parameters in the model for each parameter the table shows the estimated value and the standard error and t value for the estimate. The table also indicates the lag at which the parameter appears in the model. In this case there are two parameters in the model. The mean term is labeled MU its estimated value is 0.90280. The autoregressive parameter is labeled AR1 1 this is the coefficient of the lagged value of the change in SALES and its estimate is 0.86847. The t values provide significance tests for the parameter estimates and indicate whether some terms in the model might be unnecessary. In this case the t value for the autoregressive parameter is 15.83 so this term is highly significant. The t value for MU indicates that the mean term adds little to the model. The standard error estimates are based on large sample theory. Thus the standard errors are labeled as approximate and the standard errors and t values might not be reliable in small samples. The next part of the ESTIMATE statement output is a table of goodness-of-fit statistics which aid in comparing this model to other models. This output is shown in Figure 7.9. Figure 7.9 Goodness-of-Fit Statistics for AR 1 Model Constant Estimate 0.118749 Variance Estimate 1.15794 Std Error Estimate 1.076076 AIC 297.4469 SBC 302.6372 Number of Residuals 99 The Constant Estimate is a function of the mean term MU and the autoregressive parameters. This estimate is computed only for AR or ARMA models but not for strictly MA .