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SAS/Ets 9.22 User's Guide 42. 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 | 402 F Chapter 8 The AUTOREG Procedure the restricted model is yt xt ut To test for misspecification in the functional form the unrestricted model is p yt xtfi 2 yt ut j 2 where yt is the predicted value from the linear model and p is the power of yt in the unrestricted model equation starting from 2. The number of higher-ordered terms to be chosen depends on the discretion of the analyst. The RESET option produces test results for p 2 3 and 4. The reset test is an F statistic for testing H0 0j 0 for all j 2 . p against H1 0j 0 for at least one j 2 . p in the unrestricted model and is computed as follows _ SSEr - SSEu p - 1 F p-i n-k-p D SSEu n - k - p 1 where S SEr is the sum of squared errors due to the restricted model S SEu is the sum of squared errors due to the unrestricted model n is the total number of observations and k is the number of parameters in the original linear model. Ramsey s test can be viewed as a linearity test that checks whether any nonlinear transformation of the specified independent variables has been omitted but it need not help in identifying a new relevant variable other than those already specified in the current model. Testing for Nonlinear Dependence Heteroscedasticity Tests Portmanteau Q Test For nonlinear time series models the portmanteau test statistic based on squared residuals is used to test for independence of the series McLeod and Li 1983 Q q N N 2 y -E2E N -l where r i . v 2 EtN - 1 Vt2 - Q- Q2 t PtN i Vt2 - Q2 2 1 N q 2 _L y v 2 Nt t i This Q statistic is used to test the nonlinear effects for example GARCH effects present in the residuals. The GARCH.p q process can be considered as an ARMA max p q p process. See the section Predicting the Conditional Variance on page 407 later in this chapter. Therefore the Q statistic calculated from the squared residuals can be used to identify the order of the GARCH process. Testing F 403 Engle s Lagrange Multiplier Test for ARCH Disturbances Engle 1982 proposed a Lagrange multiplier .
