Computing the Quantiles of the Trace Statistic by Simulation Gauss file(s) coint_tracecv.g Matlab file(s) coint_tracecv.m The quantiles of the trace statistic reported in Table 18.4 for models 1 to 5 are computed by simulating the model under the null hypothesis of N − r common trends.

(a) For Model 1, simulate the following K dimensional process under the null hypothesis ∆yt = vt , vt ∼ iid N(0, V ), where V = IK and vt is (T × K) matrix which approximates the Brownian increments dB(s) and yt approximates B(s). In the computation of B and dB(s), the latter is treated as a forward difference relative to B. Compute the trace statistic LR = tr [T −1X T t=1 vty ′ t−1 ][T −2X T t=1 yt−1y ′ t−1 ] −1 [T −1X T t=1 yt−1v ′ t ]  , 100000 times and find the 90%, 95% and 99% quantiles of LR for K = 1, 2, · · · , 6 common trends.

(b) For Model 2, repeat part (a), except that B is augmented by including a constant.

(c) For Model 3, repeat part (a), except replace one of the common trends in B by a deterministic time trend and then demean B.

(d) For Model 4, repeat part (a), except augment B by including a deterministic time trend and then demean B.

(e) For Model 5, repeat part (a), except replace one of the common trends in B by a squared deterministic time trend and then detrend B by regressing B on a constant and a deterministic time trend.