Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue

I consider a bivariate stationary fractional cointegration system and I propose a quasi-maximum likelihood estimator based on the Whittle analysis of the joint spectral density of the regressor and errors. This allows to estimate jointly all parameters of interest of the model. I lead a Monte Carlo experiment to investigate the finite sample properties of this estimator when integration orders are less than 1/2. However, it is not so easy for practitioners to identify whether or not the observed time series are stationary. This issue is investigated by extending the numerical analysis to mean-reverting non-stationary region of the parameter space, although the proposed estimator is not theoretically designed to handle this case. The results display good finite sample properties in both cases, stationary and non-stationary. Thereby, it reveals that making a wrong decision on the stationarity of raw series does not lead to an erroneous conclusion. An application to the stock market synchronization is proposed to illustrate the empirical relevance of this estimator.