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SAS/ETS 9.22 User's Guide 223

SAS/Ets 9.22 User's Guide 223. 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 | 2212 F Chapter 32 The VARMAX Procedure Output 32.2.7 Proportions of Prediction Error Covariance Decomposition Proportions of Prediction Error Covariances by Variable Variable Lead yi y2 y3 yi i 1.00000 0.00000 0.00000 2 0.95996 0.01751 0.02253 3 0.94565 0.02802 0.02633 4 0.94079 0.02936 0.02985 5 0.93846 0.03018 0.03136 6 0.93831 0.03025 0.03145 y2 i 0.01754 0.98246 0.00000 2 0.06025 0.90747 0.03228 3 0.06959 0.89576 0.03465 4 0.06831 0.89232 0.03937 5 0.06850 0.89212 0.03938 6 0.06924 0.89141 0.03935 y3 i 0.07995 0.27292 0.64713 2 0.07725 0.27385 0.64890 3 0.12973 0.33364 0.53663 4 0.12870 0.33499 0.53631 5 0.12859 0.33924 0.53217 6 0.12852 0.33963 0.53185 The table in Output 32.2.8 gives forecasts and their prediction error covariances. Output 32.2.8 Forecasts Forecasts Standard Variable Obs Time Forecast Error 95 Confidence Limits y1 77 1979 1 6.54027 0.04615 6.44982 6.63072 78 1979 2 6.55105 0.05825 6.43688 6.66522 79 1979 3 6.57217 0.06883 6.43725 6.70708 80 1979 4 6.58452 0.08021 6.42732 6.74173 81 1980 1 6.60193 0.09117 6.42324 6.78063 y2 77 1979 1 7.68473 0.01172 7.66176 7.70770 78 1979 2 7.70508 0.01691 7.67193 7.73822 79 1979 3 7.72206 0.02156 7.67980 7.76431 80 1979 4 7.74266 0.02615 7.69140 7.79392 81 1980 1 7.76240 0.03005 7.70350 7.82130 y3 77 1979 1 7.54024 0.00944 7.52172 7.55875 78 1979 2 7.55489 0.01282 7.52977 7.58001 79 1979 3 7.57472 0.01808 7.53928 7.61015 80 1979 4 7.59344 0.02205 7.55022 7.63666 81 1980 1 7.61232 0.02578 7.56179 7.66286 Example 32.2 Analysis of German Economic Variables F 2213 Output 32.2.9 shows that you cannot reject Granger noncausality from y2 y 3 to y1 using the 0.05 significance level. Output 32.2.9 Granger Causality Tests Granger-Causality Wald Test Test DF Chi-Square Pr ChiSq 1 4 6.37 0.1734 Test 1 Group 1 Variables y1 Group 2 Variables y2 y3 The following SAS statements show that the variable y1 is the exogenous variable and fit the VARX 2 1 model to the data. proc varmax data use id date interval qtr model y2 y3 y1