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Averaged Periodogram Spectral Estimation with Long‐memory Conditional Heteroscedasticity

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  • Marc Henry

Abstract

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, in this paper the averaged periodogram statistic is analysed in the framework of a generalized linear process with long‐memory conditional heteroscedastic innovations according to a model specification first proposed by Robinson (Testing for strong serial correlation and dynamic conditional heteroscedasticity in multiple regression. J. Economet. 47 (1991), 67–84). 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's averaged periodogram estimate of long memory (Semiparametric analysis of long memory time series. Ann. Stat. 22 (1994), 515–39) remains consistent.

Suggested Citation

  • Marc Henry, 2001. "Averaged Periodogram Spectral Estimation with Long‐memory Conditional Heteroscedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 431-459, July.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:4:p:431-459
    DOI: 10.1111/1467-9892.00234
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    Cited by:

    1. Zevallos, Mauricio & Palma, Wilfredo, 2013. "Minimum distance estimation of ARFIMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 242-256.
    2. Pan, Qunxing & Li, Peng & Du, Xiuli, 2023. "An improved FIGARCH model with the fractional differencing operator (1-νL)d," Finance Research Letters, Elsevier, vol. 55(PB).
    3. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    4. Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, July.

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