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Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels

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Author Info
Robinson, P.M.
Henry, M.
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.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 15 (1999)
Issue (Month): 03 (June)
Pages: 299-336
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Handle: RePEc:cup:etheor:v:15:y:1999:i:03:p:299-336_15

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  1. M. Ooms & J.A. Doornik, 1999. "Inference and forecasting for fractional autoregressive integrated moving average models; with an application to US and UK inflation," Econometric Institute Report 171, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  2. Jonathan H. Wright, 2000. "Log-periodogram estimation of long memory volatility dependencies with conditionally heavy tailed returns," International Finance Discussion Papers 685, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  3. Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," CIRJE F-Series CIRJE-F-608, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  4. Rohit Deo & Clifford Hurvich & Philippe Soulier & Yi Wang, 2005. "Propagation of Memory Parameter from Durations to Counts," Econometrics 0511010, EconWPA. [Downloadable!]
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