TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 209

SAS/Ets User's Guide 209. 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 | 2072 F Chapter 32 The VARMAX Procedure Figure Parameter Estimation with Restrictions The VARMAX Procedure XLag Lag Variable xl x2 0 yi y2 - y3 - AR Lag Variable y1 y2 y3 1 yi y2 y3 Schematic Representation Variable Lag C XL0 AR1 y1 . . . y2 . .- y3 - . is 2 std error is -2 std error is between is N A The output in Figure shows the estimates of the Lagrangian parameters and their significance. Based on the p-values associated with the Lagrangian parameters you cannot reject the null hypotheses 0 2 0 012 0 and 032 0 with the significance level. Figure RESTRICT Statement Results Testing of the Restricted Parameters Parameter Estimate Standard Error t Value Pr t XL0_1_2 AR1_1_2 AR1_3_2 The TEST statement in the following example tests 03 1 0 and 0f2 0 1 2 032 0 for the VARX 1 0 model Causality Testing F 2073 proc varmax data grunfeld model y1-y3 x1 x2 p 1 test AR 1 3 1 0 test XL 0 1 2 0 AR 1 1 2 0 AR 1 3 2 0 run The output in Figure shows that the first column in the output is the index corresponding to each TEST statement. You can reject the hypothesis test p31 0 at the significance level but you cannot reject the joint hypothesis test 0 2 p12 p32 0 at the significance level. Figure TEST Statement Results The VARMAX Procedure Testing of the Parameters Test DF Chi-Square Pr ChiSq 1 1 .0001 2 3 Causality Testing The following statements use the CAUSAL statement to compute the Granger causality test for a VAR 1 model. For the Granger causality tests the autoregressive order should be defined by the P option in the MODEL statement. The variable groups are defined in the MODEL statement as well. Regardless of whether the variables specified in the GROUP1 and GROUP2 options are designated as dependent

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