Modelling stochastic volatility in asset returns using fractionally integrated semiparametric techniques

Abstract

This study estimates the order of integration in the volatility process of several exchange rates and stock returns using fractionally integrated semiparametric techniques, namely a local Whittle semiparametric estimator. The results suggest that all series can be well described in terms of I(d) statistical models, with values of d higher than 0, indicating long-memory behaviour.

Acknowledgements

Luis A. Gil-Alana gratefully acknowledges financial support from the PIUNA Project at the University of Navarra.

Notes

¹ Velasco (1999) has shown that the fractionally differencing parameter can also be consistently estimated semiparametrically in nonstationary contexts by means of tapering. See also Phillips and Shimotsu (2005).

² Some methods to calculate the optimal bandwidth numbers are examined in Delgado and Robinson (1996) and Robinson and Henry (1996). However, in the case of the Whittle estimator, the use of optimal values has not been theoretically justified. Other authors, such as Lobato and Savin (1998), use an interval of values for m, but we have preferred to report the results for the whole range of values of m.