TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 69

SAS/Ets User's Guide 69. 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 | 672 F Chapter 12 The ENTROPY Procedure Experimental Figure Prior Distribution of Parameter T For the PRIOR data set created previously the expected value of the coefficient of T is 2. The following SAS statements reestimate the parameters with a prior weight specified for each one. proc entropy data prior outest parm2 noprint priors t 0 1 2 3 4 1 intercept -100 .5 -10 0 2 10 100 model y t by by run The priors on the coefficient of T express a confident view of the value of the coefficient. The priors on INTERCEPT express a more diffuse view on the value of the intercept. The following PROC UNIVARIATE statement computes summary statistics from the estimations proc univariate data parm2 var t run The summary statistics for the distribution of the estimates of T are shown in Figure . Using Prior Information F 673 Figure Prior Information Monte Carlo Summary Prior Distribution of Parameter T The UNIVARIATE Procedure Variable t Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode . Range Interquartile Range The prior information improves the estimation of the coefficient of T dramatically. The downside of specifying priors comes when they are incorrect. For example say the priors for this model were specified as priors t -2 1 0 3 2 1 to indicate a prior centered on zero instead of two. The resulting summary statistics shown in Figure indicate how the estimation is biased away from the solution. Figure Incorrect Prior Information Monte Carlo Summary Prior Distribution of Parameter T The UNIVARIATE Procedure Variable t Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode . Range Interquartile Range The more data available for estimation the less sensitive the parameters are to the priors. If the number of observations in each sample is 50 instead of 10 then the

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