Residual-based block bootstrap for cointegration testing

Abstract

We propose a new testing procedure to determine the rank of cointegration. This new method is based on the nonparametric resampling procedure, so-called Residual-Based Block Bootstrap (RBB), which is developed by Paparoditis and Politis (2003) in the context of unit root testing. Through Monte Carlo experiments we show that, in small samples, the RBB cointegration test has good power properties in relation to the other two well-known tests for cointegration, such as the Augmented Dickey–Fuller (ADF), applied to the residual of a cointegrating regression, and the Johansen's maximum eigenvalue tests. Likewise, this article looks at the influence played by the correlation of the ‘X’ variables with the errors of the cointegrating regression on the size and power properties of the above cointegration tests. In particular, we show that, when this correlation decreases, the RBB test for cointegration is the most powerful one.

Acknowledgements

This work is an outcome of the research projects: 05838/PHCS/07 financed by ‘Programa de Generación de Conocimiento Científico de Excelencia de la Fundación Séneca, Agencia de Ciencia y Tecnología de la Región de Murcia’ and ECO2008-06238-C02-01/ECON funded by the Spanish Ministry of Education and Science and ERDF.

Notes

¹Examples of recent cointegration tests are Chigira (2008), Masuda (2008) and Oh and Soo So (2008).

²This unit root procedure is based on the block bootstrap by Künsch (1989) and Liu and Singh (1992), and it is a modification of the continuous-path block bootstrap algorithm introduced by Paparoditis and Politis (2001).

³We name d _1t  = τ₁, d _2t  = (μ₂ − γ′ μ₁) + (τ₂ − γ′₁ τ₁)t and x′ _t β = γ′ x _t as in Pesavento's (2000) model. More details about the properties of the model and its components can be found in the work of Pesavento (2004).

⁴The same argument is used in the context of the ADF test to explain why it is not possible applying it to the residuals without previously correcting its critical values.

⁵A discussion about the ‘optimal’ block size choice appears in the work of Paparoditis and Politis (2003).