SAS/Ets User's Guide 217. 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 | 2152 F Chapter 32 The VARMAX Procedure Test for the Common Trends Stock and Watson 1988 proposed statistics for common trends testing. The null hypothesis is that the k-dimensional time series yt has m common stochastic trends where m k and the alternative is that it has s common trends where s m . The test procedure of m versus s common stochastic trends is performed based on the first-order serial correlation matrix of yt. Let 0 be a k x m matrix orthogonal to the cointegrating matrix such that 0 0 0 and 0 0 Im. Let zt 00yt and wt 0 yt. Then wt ß yo ß St ß 1 XX fi ß B f i 0 Combining the expression of zt and wt zt Wt ß0 yo ß yo 0 ß 1 t X i 1 ß0 B ß B ft 0 L ßl dt C The Stock-Watson common trends test is performed based on the component wt by testing whether ß 1 has rank m against rank s. The following statements perform the Stock-Watson test for common trends proc iml sig 100 i 2 phi call varmasim y phi sigma sig n 100 initial 0 seed 45876 cn y1 y2 create simul2 from y colname cn append from y quit data simul2 set simul2 date intnx year 01jan1900 d _n_-1 format date year4. run proc varmax data simul2 model y1 y2 p 2 cointtest sw run In Figure the first column is the null hypothesis that yt has m k common trends the second column is the alternative hypothesis that yt has s m common trends the third column contains the eigenvalues used for the test statistics the fourth column contains the test statistics using AR p filtering of the data. The table shows the output of the case p 2. Vector Error Correction Modeling F 2153 Figure Common Trends Test COINTTEST SW Option The VARMAX Procedure Common Trend Test 5 H0 H1 Critical Rank m Rank s Eigenvalue Filter Value Lag 1 0 2 2 0 1 The test statistic for testing for 2 versus 1 common trends is more negative than the critical value . Therefore the test rejects the null hypothesis which means that the .
