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Download RATS Programming Manual, By Walter Enders
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IF Statements and Monte Carlo Experiments 149 Statistics on Series F Observations 50000 Sample Mean 1.6524588263 Standard Error 1.1741364996 t-Statistic 314.70023 Skewness 1.73656 Kurtosis 5.01475 Jarque-Bera 77521.44422 Variance SE of Sample Signif Level Signif Level Signif Level Signif Level Minimum 01-%ile 0.0013651902 0.1977081049 Maximum 99-%ile 14.4743025649 5.6967829958 05-%ile 0.3681509883 95-%ile 3.9233591336 10-%ile 25-%ile Median 0.5025774653 0.8187794721 1.3579015615 90-%ile 75-%ile 3.1857908038 2.1691250789 Mean (Mean=0) (Sk=0) (Ku=0) (JB=0) 1.378597 0.005251 0.00000000 0.00000000 0.00000000 0.00000000 Suppose that you estimated a series as a threshold process: ∆yt = Itρ1yt-1 + (1 – It)ρ2yt-1 + εt 1 if y t −1 ≥ 0 where: I t = 0 if y t −1 < 0 If the sample F-statistic of the null hypothesis ρ1 = ρ2 = 0 was 3.5, you would be able to reject the null hypothesis at the 10% significance level but not the 5% level. You can modify the program by (i) including an INFOBOX, (ii) obtaining the critical values for additional sample sizes, and (iii) obtaining the critical values when Chan’s (1993) method (see Section 3.1 in this chapter) is used to estimate the threshold. 5.5 Inference in a Cointegrated System This is one of my favorite programs. It illustrates a number of RATS advanced features and the folly of using traditional distribution theory to perform hypothesis tests on a cointegrating vector. Suppose that xt and yt are two non-stationary time-series variables that are cointegrated of order 1. The error-correction representation of the system is: yt = yt-1 - α1 [ β0 + yt-1 - β1xt-1 ] + A11(L)∆yt-1 + A12(L)∆xt-1 + e1t xt = xt-1 + α2[ β0 + yt-1 - β1xt-1 ] + A21(L)∆yt-1 + A22(L)∆xt-1 + e2t It is assumed that e1t and e2t are serially uncorrelated but the covariance Ee1t e2t need not be zero. As in Chapter 2, if the variances and covariance are time-invariant, we can write the variance/covariance matrix as:
