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SAS/ETS 9.22 User's Guide 115

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SAS/Ets 9.22 User's Guide 115. 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 | 1132 F Chapter 18 The MODEL Procedure data exp x 0 do time 1 to 100 if time 50 then x 1 y 35 exp 0.01 time rannor 123 x 5 output end run proc model data exp parm zo 35 b dert.z b z y z fit y init z zo chow 40 50 60 pchow 90 run The data set introduces an artificial structural change into the model the structural change effects the intercept parameter . The output from the requested Chow tests are shown in Figure 18.55. Figure 18.55 Chow s Test Results The MODEL Procedure Structural Change Test Break Test Point Num DF Den DF F Value Pr F Chow 40 2 96 12.95 .0001 Chow 50 2 96 101.37 .0001 Chow 60 2 96 26.43 .0001 Predictive Chow 90 11 87 1.86 0.0566 Profile Likelihood Confidence Intervals Wald-based and likelihood-ratio-based confidence intervals are available in the MODEL procedure for computing a confidence interval on an estimated parameter. A confidence interval on a parameter h can be constructed by inverting a Wald-based or a likelihood-ratio-based test. The approximate 100 1 a Wald confidence interval for a parameter h is f Z1-a 2a where zp is the 100pth percentile of the standard normal distribution h is the maximum likelihood estimate of h and o is the standard error estimate of h. A likelihood-ratio-based confidence interval is derived from the 2 distribution of the generalized likelihood ratio test. The approximate 1 a confidence interval for a parameter h is h 2 l h - l ff q1 1-a 21 Profile Likelihood Confidence Intervals F 1133 where qi.i- is the 1 a quantile of the 2 with one degree of freedom and 0 is the log likelihood as a function of one parameter. The endpoints of a confidence interval are the zeros of the function 0 . Computing a likelihood-ratio-based confidence interval is an iterative process. This process must be performed twice for each parameter so the computational cost is considerable. Using a modified form of the algorithm recommended by Venzon and Moolgavkar 1988 you can determine that the cost of each endpoint computation is .