TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 215

SAS/Ets User's Guide 215. 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 | 2132 F Chapter 32 The VARMAX Procedure Figure shows that the partial canonical correlations pi m between yt and yt-m are and for lags m 1 to 3. After lag m 1 the partial canonical correlations are insignificant with respect to the significance level indicating that an AR order of m 1 can be an appropriate choice. Figure Partial Canonical Correlations PCANCORR Option The VARMAX Procedure Partial Canonical Correlations Lag Correlation1 Correlation2 DF Chi-Square Pr ChiSq 1 4 .0001 2 4 3 4 The Minimum Information Criterion MINIC Method The minimum information criterion MINIC method can tentatively identify the orders of a VARMA p q process. Note that Spliid 1983 Koreisha and Pukkila 1989 and Quinn 1980 proposed this method. The first step of this method is to obtain estimates of the innovations series et from the VAR pe where pe is chosen sufficiently large. The choice of the autoregressive order pe is determined by use of a selection criterion. From the selected VAR pe model you obtain estimates of residual series Pe e yt - X p6 yt -i_ Pe t pe i --- t i 1 In the second step you select the order p q of the VARMA model for p in pmin pmax and q in qmin qmax P q yt S O yt-i - 0i it -i et which minimizes a selection criterion like SBC or HQ. The following statements use the MINIC option to compute a table that contains the information criterion associated with various AR and MA orders proc varmax data simul1 model y1 y2 p 1 noint minic p 3 q 3 run Figure shows the output associated with the MINIC option. The criterion takes the smallest value at AR order 1. VAR and VARX Modeling F 2133 Figure MINIC Option The VARMAX Procedure Minimum Information Criterion Based on AICC Lag MA 0 MA 1 MA 2 MA 3 AR 0 AR 1 AR 2 AR 3

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