TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 116

SAS/Ets User's Guide 116. 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 | 1142 F Chapter 18 The MODEL Procedure MA Initial Conditions The initial lags of the error terms of MA models can also be modeled in different ways. The following moving-average error start-up paradigms are supported by the ARIMA and MODEL procedures ULS CLS ML unconditional least squares conditional least squares maximum likelihood The conditional least squares method of estimating moving-average error terms is not optimal because it ignores the start-up problem. This reduces the efficiency of the estimates although they remain unbiased. The initial lagged residuals extending before the start of the data are assumed to be 0 their unconditional expected value. This introduces a difference between these residuals and the generalized least squares residuals for the moving-average covariance which unlike the autoregressive model persists through the data set. Usually this difference converges quickly to 0 but for nearly noninvertible moving-average processes the convergence is quite slow. To minimize this problem you should have plenty of data and the moving-average parameter estimates should be well within the invertible range. This problem can be corrected at the expense of writing a more complex program. Unconditional least squares estimates for the MA 1 process can be produced by specifying the model as follows yhat . compute structural predicted value here . if _obs_ 1 then do h sqrt 1 ma1 2 y yhat y - yhat h end else do g ma1 zlag1 h h sqrt 1 ma1 2 - g 2 y yhat g zlag1 y - yhat - g zlag1 h end Moving-average errors can be difficult to estimate. You should consider using an AR p approximation to the moving-average process. A moving-average process can usually be well-approximated by an autoregressive process if the data have not been smoothed or differenced. The AR Macro The SAS macro AR generates programming statements for PROC MODEL for autoregressive models. The AR macro is part of SAS ETS software and no special options need to

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