Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels

P. M. Robinson, M. Henry

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

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 heteroskedasticity. We show that a leading semiparametric estimate, the Gaussian or local Whittle one, can be consistent and have the same limiting distribution under conditional heteroskedasticity as under the conditional homoskedasticity assumed by Robinson (1995, Annals of Statistics 23, 1630-61). Indeed, noting that long memory has been observed in the squares of financial time series, we allow, under regularity conditions, for conditional heteroskedasticity of the general form introduced by Robinson (1991, Journal of Econometrics 47, 67-84), which may include long memory behavior for the squares, such as the fractional noise and autoregressive fractionally integrated moving average form, and also standard short memory ARCH and GARCH specifications.

Original languageEnglish (US)
Pages (from-to)299-336
Number of pages38
JournalEconometric Theory
Volume15
Issue number3
DOIs
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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