In the previous chapters all the reasoning has proceeded on the asymptotic theories, while the methods derived there anticipate their applications to macroeco-nomic studies involving about 100 to 200 quarterly observations. The present chapter presents our simulation studies for the case where n = 2, p = 2, T = 100 or 200, and S H = [t, dt (b)] with b = 0.5. Section 8.1 will describe seven DGPs that incorporate a variety of structures of deterministic trends as well as different cointegration structures. Section 8.2 will give a detailed description of the trend test for I(0) for the special case of n, p, and S H, because the test was only outlined in Section 6.1 for the general case. Section 8.3 will begin with the reiteration of the asymptotic reasoning on the special case of n, p, and S H, which leads to a table of probabilities, Table 8.4, which we should expect if we had an infinite sample size. The table is arranged so that it can be easily compared with the tables of probabilities produced by simulations on finite sample sizes. In Section 8.3 we shall also give instruction on the last grouping method, which was left unclear in Chapter 7. Section 8.4 will present our simulations studies. The design of simulations incorporates data-dependence of the critical values of the trend test for I(1). Some discrepancies are discovered between the asymptotic theory and the simulation results with T = 100 and 200, and the discrepancies are analysed. Section 8.5 will present an example of applications to Japanese macroeconomic time series.
KeywordsUnit Root Unit Root Test Grouping Method Asymptotic Theory Trend Test
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