Robust Inference in Models of Cointegration

Abstract

This paper introduces a test statistic that is robust to serial correlation/heteroskedasticity of unknown form in a single-equation cointegration environment that incorporates linear polynomial trend functions. The standard approach used to deal with heteroskedasticity and serial correlation in models of this type has been to estimate the correlation structure of the error terms. While this approach generates consistent estimates of the correlation structure, the possibility of substantial size distortions in finite samples remains. The test proposed in this paper eliminates the need to estimate the correlation structure, and hence removes an important source of size distortions. The development of the new test relies upon a data-dependent transformation of the ordinary least squares estimates of the parameters. The test can also be employed to conduct inference on the trend function, on the cointegration vector in a cointegration relationship, and on the parameters of the deterministic trend function of a univariate time series. Extensive simulation experiments investigate the properties of the new test statistic in finite samples. These reveal that size distortions are generally less than those of tests currently employed in the literature; moreover, there is no substantial reduction in power.

JEL Classification: C12, C13, C14, C22