Bootstrap and fast double bootstrap tests of cointegration rank with financial time series
The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. Bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test are introduced and evaluated by Monte Carlo simulation experiments. It is found that the performance of the ordinary (single) bootstrap test is in most cases good in terms of the size of the test. The FDB produces a further improvement in cases where the performance of the asymptotic test is unsatisfactory and the single bootstrap test overrejects noticeably. The FDBÂ is shown to be a useful supplement to the single bootstrap as a tool for determining the cointegration rank. The tests are applied to US interest rates and international stock prices series. By simulating the data assuming that the cointegration rank is known, it is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.
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