Bootstrap LR tests of stationarity, common trends and cointegration

Fabio Busetti and Silvestro Di Sanzo

No 799, Temi di discussione (Economic working papers) from Bank of Italy, Economic Research and International Relations Area

Abstract: The paper considers likelihood ratio (LR) tests of stationarity, common trends and cointegration for multivariate time series. As the distribution of these tests is not known, a bootstrap version is proposed via a state space representation. The bootstrap samples are obtained from the Kalman filter innovations under the null hypothesis. Monte Carlo simulations for the Gaussian univariate random walk plus noise model show that the bootstrap LR test achieves higher power for medium-sized deviations from the null hypothesis than a locally optimal and one-sided LM test, that has a known asymptotic distribution. The power gains of the bootstrap LR test are significantly larger for testing the hypothesis of common trends and cointegration in multivariate time series, as the alternative asymptotic procedure -obtained as an extension of the LM test of stationarity- does not possess properties of optimality. Finally, it is showed that the (pseudo) LR tests maintain good size and power properties also for non-Gaussian series. As an empirical illustration, we find evidence of two common stochastic trends in the volatility of the US dollar exchange rate against european and asian/pacific currencies.

Keywords: Kalman filter; state-space models; unit roots (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
Date: 2011-03
New Economics Papers: this item is included in nep-ecm and nep-ets
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