Averaged Periodogram Spectral Estimation With Long Memory Conditional Heteroscedasticity

The empirical relevance of long memory conditional heteroscedasticity has emerged in a variety of studies of long time series of high frequency financial measurements. A reassessment of the applicability of existing semiparametric frequency domain tools for the analysis of time dependence and long run behaviour of time series is therefore warranted. To that end, this paper analyses the averaged periodogram statistic in the framework of a generalized linear process with long memory conditional heteroscedastic innovations according to a model specification first proposed by Robinson (1991). It is shown that the averaged periodogram estimate of the spectral density of a short memory process remains asymptotically normal with unchanged asymptotic variance under mild moment conditions, and that for strongly dependent processes, Robinson (1994)'s averaged periodogram estimate of long memory remains consistent. 1 This research was carried out at the Financial Markets Group of the London Sch..