TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 203

SAS/Ets User's Guide 203. 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 | 2012 F Chapter 31 The UCM Procedure First the various statistics of fit that are computed using the prediction errors yt yt are considered. In these formulas n is the number of nonmissing prediction errors and k is the number of fitted parameters in the model. Moreover the sum of squared errors SSE 22 yt _ yt 2 and the total sum of squares for the series corrected for the mean SST 22 yt _ y 2 where y is the series mean and the sums are over all the nonmissing prediction errors. Mean Squared Error The mean squared prediction error MSE 1 SSE Root Mean Squared Error The root mean square error RMSE VMSE Mean Absolute Percent Error The mean absolute percent prediction error MAPE 1 22 i I yt yt yt I. The summation ignores observations where yt 0. R-square The R-square statistic R2 1 SSE SST. If the model fits the series badly the model error sum of squares SSE might be larger than SST and the R-square statistic will be negative. Adjusted R-square The adjusted R-square statistic 1 - n r 1 - R2 Amemiya s Adjusted R-square Amemiya s adjusted R-square 1 nCk 1 _ R2 Random Walk R-square The random walk R-square statistic Harvey s R-square statistic that uses the random walk model for comparison 1 nj r SSE RWSSE where RWSSE P 2 yt _ yt-1 _ 2 and i pn 2 yt - yt-i Maximum Percent Error The largest percent prediction error 100 max yt yt yt . In this computation the observations where yt 0 are ignored. The likelihood-based fit statistics are reported separately see the section The UCMs as State Space Models on page 1979 . They include the full log likelihood L1 the diffuse part of the log likelihood the normalized residual sum of squares and several information criteria AIC AICC HQIC BIC and CAIC. Let q denote the number of estimated parameters n be the number of nonmissing measurements in the estimation span and d be the number of diffuse elements in the initial state vector that are successfully initialized during the Kalman filtering process. Moreover let n n d . The reported .

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