tailieunhanh - SAS/ETS 9.22 User's Guide 113

SAS/Ets User's Guide 113. 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 | 1112 F Chapter 18 The MODEL Procedure Error Covariance Structure Specification One of the key assumptions of regression is that the variance of the errors is constant across observations. Correcting for heteroscedasticity improves the efficiency of the estimates. Consider the following general form for models q y xt ff et t Ht ht Ht t 2 Jhp. 0 . 0 0 ph 2 . 0 . . . _ 0 0 . Jh g g yt Xt 0 where et N 0 S . For models that are homoscedastic ht 1 If you have a model that is heteroscedastic with known form you can improve the efficiency of the estimates by performing a weighted regression. The weight variable using this notation would be 1 Ph. If the errors for a model are heteroscedastic and the functional form of the variance is known the model for the variance can be estimated along with the regression function. To specify a functional form for the variance assign the function to an variable where var is the equation variable. For example if you want to estimate the scale parameter for the variance of a simple regression model y a x b you can specify proc model data s y a x b sigma 2 fit y Consider the same model with the following functional form for the variance ht a2 x2 This would be written as Error Covariance Structure Specification F 1113 proc model data s y a x b sigma 2 x 2 alpha fit y There are three ways to model the variance in the MODEL procedure feasible generalized least squares generalized method of moments and full information maximum likelihood. Feasible GLS A simple approach to estimating a variance function is to estimate the mean parameters fi by using some auxiliary method such as OLS and then use the residuals of that estimation to estimate the parameters 0 of the variance function. This scheme is called feasible GLS. It is possible to use the residuals from an auxiliary method for the purpose of estimating 0 because in many cases the residuals consistently estimate the error terms. For all estimation methods except GMM and FIML .