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SAS/Ets 9.22 User's Guide 40. 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 | 382 F Chapter 8 The AUTOREG Procedure If the NOINT option is requested no correction for the transformed intercept is made. The Reg RSQ is a measure of the fit of the structural part of the model after transforming for the autocorrelation and is the R-Square for the transformed regression. The regression R-Square and the total R-Square should be the same when there is no autocorrelation correction OLS regression . Mean Absolute Error and Mean Absolute Percentage Error The mean absolute error MAE is computed as 1 T MAE D -Y et I t 1 where et are the estimated model residuals and is the number of observations. The mean absolute percentage error MAPE is computed as T 1 2 I Z7 . I mape D - iyt JLd t 1 t1 where et are the estimated model residuals yt are the original response variable observations ht o D 1 if Lt 0 yt 0 et yt D 0 if yt D 0 and is the number of nonzero original response variable observations. Calculation of Recursive Residuals and CUSUM Statistics The recursive residuals wt are computed as et yt - x rt-1 q-1 xi j i t-i X x y i 1 rt-i vt 1 x t -i Xt X X _ 1 Note that the first .t can be computed for t p 1 where p is the number of regression coefficients. As a result first p recursive residuals are not defined. Note also that the forecast error variance of et is the scalar multiple of vt such that V.et a2vt. The CUSUM and CUSUMSQ statistics are computed using the preceding recursive residuals. w CUSUMt i k 1 aw Goodness-of-fit Measures and Information Criteria F 383 CUSUMSQt r k 1 W E fc i wi where Wi are the recursive residuals . D T k i .w - w 2 .T - k - 1 1 W D T - k T X Wi i k 1 and k is the number of regressors. The CUSUM statistics can be used to test for misspecification of the model. The upper and lower critical values for CUSUMt are a pT - k 2 k r L .T - k 2j where a 1.143 for a significance level 0.01 0.948 for 0.05 and 0.850 for 0.10. These critical values are output by the CUSUMLB and CUSUMUB options for the significance level specified by the .
