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Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility

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  • Eric Hillebrand

    (Department of Economics, Louisiana State University)

  • Marcelo Cunha Medeiros

    (Department of Economics, PUC-rio)

Abstract

We study the simultaneous occurrence of long memory and nonlinear effects, such as structural breaks and thresholds, in autoregressive moving average (ARMA) time series models and apply our modeling framework to series of daily realized volatility. Asymptotic theory for the quasi-maximum likelihood estimator is developed and a sequence of model specification tests is described. Our framework allows for general nonlinear functions, including smoothly changing intercepts. The theoretical results in the paper can be applied to any series with long memory and nonlinearity. We apply the methodology to realized volatility of individual stocks of the Dow Jones Industrial Average during the period 1995 to 2005. We find strong evidence of nonlinear effects and explore different specifications of the model framework. A forecasting exercise demonstrates that allowing for nonlinearities in long memory models yields significant performance gains.

Suggested Citation

  • Eric Hillebrand & Marcelo Cunha Medeiros, 2010. "Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility," Textos para discussão 578, Department of Economics PUC-Rio (Brazil).
    • Handle: RePEc:rio:texdis:578
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    3. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
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    5. Nima Nonejad, 2013. "Long Memory and Structural Breaks in Realized Volatility: An Irreversible Markov Switching Approach," CREATES Research Papers 2013-26, Department of Economics and Business Economics, Aarhus University.
    6. De Santis, Roberto A. & Stein, Michael, 2016. "Correlation changes between the risk-free rate and sovereign yields of euro area countries," Working Paper Series 1979, European Central Bank.

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    Keywords

    Realized volatility; structural breaks; smooth transitions; nonlinear models; long memory; persistence.;
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