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SAS/Ets 9.22 User's Guide 222. 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 | 2202 F Chapter 32 The VARMAX Procedure Output 32.1.11 shows the innovation covariance matrix estimates the various information criteria results and the tests for white noise residuals. The residuals have significant correlations at lag 2 and 3. The Portmanteau test results into significant. These results show that a VECM 3 model might be better fit than the VECM 2 model is. Output 32.1.11 Diagnostic Checks Covariances of Innovations Variable yi y2 y3 y4 yi 0.00005 0.00001 -0.00001 -0.00000 y2 0.00001 0.00007 0.00002 0.00001 y3 -0.00001 0.00002 0.00007 0.00002 y4 -0.00000 0.00001 0.00002 0.00002 Information Criteria AICC -40.6284 HQC -40.4343 AIC -40.6452 SBC -40.1262 FPEC 2.23E-18 Schematic Representation of Cross Correlations of Residuals Variable Lag 0 1 2 3 4 5 6 y1 . . . .-- . y2 . y3 . .-. . -. . y4 . . . . is 2 std error - is -2 std error . is between Portmanteau Test for Cross Correlations of Residuals Up To Lag DF Chi-Square Pr ChiSq 3 16 53.90 .0001 4 32 74.03 .0001 5 48 103.08 .0001 6 64 116.94 .0001 Example 32.1 Analysis of U.S. Economic Variables F 2203 Output 32.1.12 describes how well each univariate equation fits the data. The residuals for y3 and y4 are off from the normality. Except the residuals for y3 there are no AR effects on other residuals. Except the residuals for y4 there are no ARCH effects on other residuals. Output 32.1.12 Diagnostic Checks Continued Univariate Model ANOVA Diagnostics Standard Variable R-Square Deviation F Value Pr F yi 0.6754 0.00712 32.51 .0001 y2 0.3070 0.00843 6.92 .0001 y3 0.1328 0.00807 2.39 0.0196 y4 0.0831 0.00403 1.42 0.1963 Univariate Model White Noise Diagnostics Variable Durbin Watson Normality ARCH Chi-Square Pr ChiSq F Value Pr F y1 2.13418 7.19 0.0275 1.62 0.2053 y2 2.04003 1.20 0.5483 1.23 0.2697 y3 1.86892 253.76 .0001 1.78 0.1847 y4 1.98440 105.21 .0001 21.01 .0001 Univariate Model AR Diagnostics Variable AR1 AR2 AR3 AR4 F Value Pr F F Value Pr F F Value Pr F F Value Pr F y1 0.68 0.4126 2.98 0.0542 2.01
