Integrated Modified OLS estimation of cointegrating regressions with deterministically trending integrated regressors and residual-based tests for cointegration

Resumen

In this paper we discuss the asymptotically almost efficient estimation of a univariate static cointegrating regression relationship when we take into account the deterministic structure of the integrated regressors, in a slightly more general framework that considered by Hansen (1992). After reviewing the properties of OLS and Fully Modified OLS (FM-OLS) estimation in this framework, we consider the analysis of the recently proposed Integrated Modified OLS (IM-OLS) estimator by Vogelsang and Wagner (2011) of the cointegrating vector and propose a new proper specification of the integrated modified cointegrating regression equation. This alternative method of bias removal has the advantage over the existing methods that does not require any tuning parameters, such as kernel functions and bandwidths, or lags. Also, based on the sequence of IM-OLS residuals, we propose some new test statistics based on different measures of excessive fluctuation for testing the null hypothesis of cointegration against the alternative of no cointegration. For these test statistics we derive their asymptotic null and alternative distributions, provide the relevant quantiles of the null distribution, and study their finite sample power performance under no cointegration through a simulation experiment.