Robust Multivariate Local Whittle Estimation and Spurious Fractional Cointegration

This paper derives a multivariate local Whittle estimator for the memory parameter of a possibly long memory process and the fractional cointegration vector robust to low frequency contaminations. This estimator as many other local Whittle based procedures requires a priori knowledge of the cointegration rank. Since low frequency contaminations bias inference on the cointegration rank, we also provide a robust estimator of the cointegration rank. As both estimators are based on the trimmed periodogram we further derive some insights in the behaviour of the periodogram of a process under very general types of low frequency contaminations. An extensive Monte Carlo exercise shows the applicability of our estimators in finite samples. Our procedures are applied to realized betas of two American energy companies discovering that the series are fractionally cointegrated. As the series exhibit low frequency contaminations, standard procedures are unable to detect this relation.