1999 Reports

Averaged Periodogram Spectral Estimation with Long Memory Conditional Heteroscedasticity

Henry, Marc

Semiparametric spectral methods seem particularly appropriate for the analysis of long financial time series, providing they are robust to a variety of forms of conditional heteroscedasticity, which is generally recognized as a dominant feature of financial returns. This paper analyses the averaged periodogram statistic in the framework of a generalized linear process with (possibly long memory) conditional heteroscedasticity in the innovations. It is shown that the averaged periodogram statistic is appropriate for a symptotically normal estimation of the spectrum of a weakly dependent process at frequency zero and for consistent estimation of long memory and stationary cointegration in strongly dependent processes. The asymptotic results are coupled with extensive small sample investigations of the performance of the estimates considered.