TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 138

SAS/Ets User's Guide 138. 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 | 1362 F Chapter 19 The PANEL Procedure As long as the following is true then you are assured that the OLS estimate is consistent and unbiased p im n X 0 If the regressors are nonrandom then it is possible to write the variance of the estimated j as the following Var j - jj X0 X -1X QX X0X 1 The effect of structure in the variance covariance matrix can be ameliorated by using generalized least squares GLS provided that Q-1 can be calculated. Using Q-1 you premultiply both sides of the regression equation Q-1y 1 . C Q-1e The resulting GLS j is j X0 1X 1X Q Using the GLS j you can write j X0 -1X 1X0 Q-1y X0 -1X 1X0 Q-1 X C Q 1 C X0 -1X 1X0Q-1e The resulting variance expression for the GLS estimator is Var j - j X0Q 1X 1X0Q-WQ_1X X Q 1X 1 X0 Q 1X 1X0 Q 1QQ 1X X0 Q 1X 1 X0 Q 1X 1 The difference in variance between the OLS estimator and the GLS estimator can be written as X0X -1X0QX X0X 1 - X0Q 1 X 1 By the Gauss Markov Theory the difference matrix must be positive definite under most circumstances zero if OLS and GLS are the same when the usual classical regression assumptions are met . Thus OLS is not efficient under a general error structure. It is crucial to realize is that OLS does not produce biased results. It would suffice if you had a method for estimating a consistent covariance matrix and you used the OLS j. Estimation of the Q matrix is by no means simple. The matrix is square and has M2 elements so unless some sort of structure is assumed it becomes an impossible problem to solve. However the heteroscedasticity can have quite a general structure. White 1980 shows that it is not necessary to have a consistent estimate of Q. On the contrary it suffices to get an estimate of the middle expression. That is you need an estimate of A X0 QX This matrix A is easier to estimate because its dimension is K. PROC PANEL provides the following classical HCCME estimators The matrix A is approximated by Heteroscedasticity-Corrected Covariance Matrices F 1363 HCCME N0 This is

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• Hướng dẫn sử dụng SAS ETS
• các mô hình phân tích tài chính
• báo cáo tài chính
• phân tích đầu tư
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