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Gaussian inference on certain long-range dependent volatility models


  • Paolo Zaffaroni

    () (Banca d'Italia)


For a class of long memory volatility models, we establish the asymptotic distribution theory of the Gaussian estimator and the Lagrange multiplier test. Both the case of estimation of martingale difference and ARMA levels are considered. A Montecarlo exercise is presented to assess the small sample properties of the Gaussian estimator and the Lagrange multiplier test. An empirical application, using foreign exchange rates and stock index returns, suggests the potential of these models to capture the dynamic features of the data.

Suggested Citation

  • Paolo Zaffaroni, 2003. "Gaussian inference on certain long-range dependent volatility models," Temi di discussione (Economic working papers) 472, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_472_03

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    References listed on IDEAS

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    Cited by:

    1. Peter M Robinson & Paolo Zaffaroni, 2005. "Pseudo-Maximum Likelihood Estimation of ARCH(8) Models," STICERD - Econometrics Paper Series 495, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Artiach, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
    3. Robinson, Peter M. & Zafaroni, Paolo, 2005. "Pseudo-maximum likelihood estimation of ARCH models," LSE Research Online Documents on Economics 4544, London School of Economics and Political Science, LSE Library.
    4. Quan-Hoang Vuong, 2004. "Analyses on Gold and US Dollar in Vietnam's Transitional Economy," Working Papers CEB 04-033.RS, ULB -- Universite Libre de Bruxelles.
    5. 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.
    6. Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
    7. Jean-Marc Bardet & Paul Doukhan & José Rafael León, 2008. "Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 906-945, September.
    8. Robinson, Peter M. & Zaffaroni, Paolo, 2005. "Pseudo-maximum likelihood estimation of ARCH(∞) models," LSE Research Online Documents on Economics 58182, London School of Economics and Political Science, LSE Library.
    9. Artiach, Miguel, 2012. "Leverage, skewness and amplitude asymmetric cycles," MPRA Paper 41267, University Library of Munich, Germany.

    More about this item


    volatility model; nonlinear moving average model; long memory; Whittle estimation; asymptotic distribution theory;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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