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Refined Inference on Long Memory in Realized Volatility

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Abstract

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et al. (2004)). The present paper provides some analytical explanations for this evidence and shows how recent results in Lieberman and Phillips (2004a, 2004b) can be used to refine statistical inference about d with little computational effort. In contrast to standard asymptotic normal theory now used in the literature which has an O(n-1/2) error rate on error rejection probabilities, the asymptotic approximation used here has an error rate of o(n-1/2). The new formula is independent of unknown parameters, is simple to calculate and highly user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et. al. (2001) and Martens et. al. (2004) differ significantly from the lower boundary (d = 0.5) of nonstationary long memory.

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  • Offer Lieberman & Peter C. B. Phillips, 2006. "Refined Inference on Long Memory in Realized Volatility," Cowles Foundation Discussion Papers 1549, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1549
    Note: CFP 1248.
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    Cited by:

    1. Lieberman, Offer & Phillips, Peter C.B., 2008. "A complete asymptotic series for the autocovariance function of a long memory process," Journal of Econometrics, Elsevier, vol. 147(1), pages 99-103, November.
    2. Bauwens, Luc & Chevillon, Guillaume & Laurent, Sébastien, 2023. "We modeled long memory with just one lag!," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España.
    4. Rossi, Eduardo & Santucci de Magistris, Paolo, 2013. "Long memory and tail dependence in trading volume and volatility," Journal of Empirical Finance, Elsevier, vol. 22(C), pages 94-112.
    5. Zhanglong Wang & Kent Wang & Zheyao Pan, 2015. "Conditional equity risk premia and realized variance jump risk," Australian Journal of Management, Australian School of Business, vol. 40(2), pages 295-317, May.
    6. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    7. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    8. Matteo Luciani & David Veredas, "undated". "A simple model for vast panels of volatilities," ULB Institutional Repository 2013/136239, ULB -- Universite Libre de Bruxelles.
    9. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    10. Tian, Fengping & Yang, Ke & Chen, Langnan, 2017. "Realized volatility forecasting of agricultural commodity futures using the HAR model with time-varying sparsity," International Journal of Forecasting, Elsevier, vol. 33(1), pages 132-152.
    11. Stefano Grassi & Nima Nonejad & Paolo Santucci De Magistris, 2017. "Forecasting With the Standardized Self‐Perturbed Kalman Filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 318-341, March.
    12. Luis F. Espinoza-Audelo & Maricruz Olazabal-Lugo & Fabio Blanco-Mesa & Ernesto León-Castro & Victor Alfaro-Garcia, 2020. "Bonferroni Probabilistic Ordered Weighted Averaging Operators Applied to Agricultural Commodities’ Price Analysis," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    13. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    14. Chevillon, Guillaume & Hecq , Alain & Laurent, Sébastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    15. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    16. J. Arteche, 2012. "Semiparametric Inference in Correlated Long Memory Signal Plus Noise Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 440-474.
    17. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    18. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
    19. Ding, Yi & Kambouroudis, Dimos & McMillan, David G., 2021. "Forecasting realised volatility: Does the LASSO approach outperform HAR?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    20. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.

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    More about this item

    Keywords

    ARFIMA; Edgeworth expansion; Fourier integral expansion; Fractional differencing; Improved inference; Long memory; Pivotal statistic; Realized volatility; Singularity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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