Frequency domain principal components estimation of fractionally cointegrated processes: Some new results and an application to stock market volatility

In this paper we present new results for the frequency domain principal components estimator of the cointegration space for stationary long memory processes of Morana [Appl. Econ. Lett. 11 (2004) 837], concerning asymptotic properties, identification of the cointegration space and the linkage with the frequency domain least-squares estimator. An application of the approach to stock market volatility data shows that the methodology can effectively be employed for the modelling of long-run relationships, which could not be handled using the standard I(1)-I(0) cointegration approach.