Bootstrap cointegration testing

Abstract

This work assesses the power and size properties of the wild bootstrap implementation of Johansen’s test for cointegration for a variety of realistic data generating processes using simulations on systems with random coefficients. A VAR(2) is used, with parameters generated randomly (but under some restrictions). We construct innovations processes with GARCH(1,1), EGARCH(1,1) and SARV(1,1) variances, as well as with outliers and regime shifts in the variance. We find that the wild bootstrap test significantly outperforms Johansen’s test when innovations exhibit conditional heteroskedasticity or stochastic volatility but not when innovations have outliers or regime shifts. Also, we find a significant tendency for both tests to underestimate the cointegrating rank, which somewhat contradicts current literature (probably associated to our choice of intervals from which parameters are drawn).