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SAS/ETS 9.22 User's Guide 129

SAS/Ets 9.22 User's Guide 129. 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 | 1272 F Chapter 18 The MODEL Procedure starts 1 - d y1 d y2 Resulting log-likelihood function logL 1 2 log 2 3.1415 log sig1 2 1-d 2 sig2 2 d 2 resid.starts 1 sig1 2 1-d 2 sig2 2 d 2 resid.starts errormodel starts general logL fit starts method marquardt converge 1.0e-5 Test for significant differences in the parms test int1 int2 lm test b11 b21 lm test b13 b23 lm test sig1 sig2 lm run Four TEST statements are added to test the hypothesis that the parameters are the same in both regimes. The parameter estimates and ANOVA table from this run are shown in Output 18.13.1. Output 18.13.1 Parameter Estimates from the Switching Regression Switching Regression Example The MODEL Procedure Nonlinear Liklhood Summary of Residual Errors DF DF Adj Equation Model Error SSE MSE R-Square R-Sq starts 9 304 85878.0 282.5 0.7806 0.7748 Nonlinear Liklhood Parameter Estimates Parameter Estimate Approx Std Err t Value Approx Pr t sigl 15.47484 0.9476 16.33 .0001 sig2 19.77808 1.2710 15.56 .0001 intl 32.82221 5.9083 5.56 .0001 bll 0.73952 0.0444 16.64 .0001 b13 -15.4556 3.1912 -4.84 .0001 int2 42.73348 6.8159 6.27 .0001 b21 0.734117 0.0478 15.37 .0001 b23 -22.5184 4.2985 -5.24 .0001 P 25.94712 8.5205 3.05 0.0025 The test results shown in Output 18.13.2 suggest that the variance of the housing starts SIG1 and SIG2 are significantly different in the two regimes. The tests also show a significant difference in the AR term on the housing starts. Example 18.14 Simulating from a Mixture of Distributions F 1273 Output 18.13.2 Test Results for Switching Regression Test Results Test Type Statistic Pr ChiSq Label Test0 L.M. i.00 0.3185 int1 int2 Testi L.M. 15636 .0001 b11 b21 Test2 L.M. 1.45 0.2280 b13 b23 Test3 L.M. 4.39 0.0361 sig1 sig2 Example 18.14 Simulating from a Mixture of Distributions This example illustrates how to perform a multivariate simulation by using models that have different error distributions. Three models are used. The first model has t distributed errors. The second model .