Robinson, Peter M. and Henry, Marc (1998) Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels. Econometrics; EM/1998/357 (EM/98/357). Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.
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Abstract
Semiparametric estimates of long memory seem useful in the analysis of long financial time series because they are consistent under much broader conditions than parametric estimates. However, recent large sample theory for semiparametric estimates forbids conditional heteroscedasticity. We show that a leading semiparametric estimate, the Gaussian or local Whittle one, can be consistent and have the same limiting distribution under conditional heteroscedasticity as under conditional homoscedasticity assumed by Robinson (1995a). Indeed, noting that long memory has been observed in the squares of financial time series, we allow, under regularity conditions, for conditional heteroscedasticity of the general form introduced by Robinson (1991) which may include long memory behaviour for the squares, such as the fractional noise and autoregressive fractionally integrated moving average form, as well as standard short memory ARCH and GARCH specifications.
| Item Type: | Monograph (Discussion Paper) |
|---|---|
| Official URL: | http://sticerd.lse.ac.uk |
| Additional Information: | © 1998 P M Robinson and M Henry |
| Divisions: | Economics STICERD |
| Subjects: | H Social Sciences > HB Economic Theory |
| JEL classification: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation |
| Date Deposited: | 27 Apr 2007 |
| Last Modified: | 13 Sep 2024 19:39 |
| URI: | http://eprints.lse.ac.uk/id/eprint/2022 |
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