Replicate the results of Example 19.2 using the same simulation design. In an application of the t-test

Replicate the results of Example 19.2 using the same simulation design.

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In an application of the t-test of independence using the randomization method of Proposition 19.3, we applied the test to pairs of AR(1) (autoregressive model order 1) time series. The AR(1) data with total length N = 2500 was generated from the model Xt = AX-1+et, where Xt is a vector of length 2, A is a matrix of autoregressive coefficients, and et R is a noise vector with mean 0. (For simplicity we let et be Gaussian, but the method is applicable for non-normal error distributions as well.) The bivariate AR(1) model parameters used in this simulation are A = ( .25 0 0 .25 1 Cov(e) = ( + 1 ), T and the length of subsequences is p = 100. The estimates of power for varying r are shown in Figure 19.1, with error bars at 2 standard errors. These es- timates are computed as the proportion of significant t-tests of independence in 2000 replications (significance level 10%). Figure 19.1 summarizes the sim- ulation results for two cases: sample size n = 25 and n = 50. (The length N = 2500 for this example was chosen to match approximately the length of the DJIA data in Example 19.3). T-test, N= 2500 p= 100 power 0.2 0.4 0.6 0.8 1.0 Jel Her K KH KH KH KH -n= 50 An= 25 r 0.0 00 -0.4 -0.2 0.0 0.2 0.4