The Size and Power of Bootstrap and Bartlett-Corrected Tests of Hypotheses on the Cointegrating Vectors

Abstract

In this paper we compare Bartlett-corrected, bootstrap, and fast double bootstrap tests on maximum likelihood estimates of cointegration parameters. The key result is that both the bootstrap and the Bartlett-corrected tests must be based on the unrestricted estimates of the cointegrating vectors: procedures based on the restricted estimates have almost no power. The small sample size bias of the asymptotic test appears so severe as to advise strongly against its use with the sample sizes commonly available; the fast double bootstrap test minimizes size bias, while the Bartlett-corrected test is somehow more powerful.Bartlett correction, Bootstrap, Cointegration, Fast double bootstrap,

Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

“…Previous simulation studies of bootstrap tests on co-integrating relations in VAR models include Fachin (2000), Gredenhoff and Jacobson (2001), and Omtzigt and Fachin (2006). Compared to these, the Monte Carlo simulation study reported here differs substantially.…”

“…resampling, but instead drawn from a Gaussian distribution with covariance matrixΩ. Finally, Omtzigt and Fachin (2006) compare the aforementioned tests with focus on the unrestricted bootstrap.…”

“…However, as is well known, the finitesample properties of these tests can be quite poor, much like in the case of rank determination. Currently there are two dominating approaches to this in the literature: one is to apply Bartlett corrections as in Johansen (2000Johansen ( , 2002a and the other is to base inference on a bootstrap scheme where the VAR model is estimated unrestrictedly (i.e., without imposing the null hypothesis) as in Omtzigt and Fachin (2006). Unfortunately, both approaches tend to be unreliable in terms of size, in particular in those cases where also the asymptotic test fails most severely.…”

Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes

“…They prove bootstrap consistency not only for the OLS estimator and corresponding test statistics, but also for the case of asymptotically efficient estimation and hypothesis testing. Size and power properties of bootstrap hypotheses tests on cointegrating vectors have been compared with Bartlett‐corrected tests in Omtzigt and Fachin () where it is pointed out that both types of tests must be based on the unrestricted estimates of the cointegrating vectors not to lose power. In a reduced rank VAR model, Swensen () applied a residual‐based bootstrap procedure for testing and determining the cointegration rank.…”

“…They prove bootstrap consistency not only for the OLS estimator and corresponding test statistics, but also for the case of asymptotically efficient estimation and hypothesis testing. Size and power properties of bootstrap hypotheses tests on cointegrating vectors have been compared with Bartlett-corrected tests in Omtzigt and Fachin (2006) where it is pointed out that both types of tests must be based on the unrestricted estimates of the cointegrating vectors not to lose power. In a reduced the m 2 -dimensional vector that contains the last m 2 D m m 1 coordinates of X t for some 0 Ä m 1 Ä m. In this section, we assume that ¹X t ; t 2 N 0 º is a so-called m-dimensional, full-rank random walk, that is, X t follows the model X t D X t 1 C U t ; t 2 N;…”