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Modelling realized variance when returns are serially correlated
[Modellierung realisierter Varianz bei autokorrelierten Erträgen]

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  • Oomen, Roel C. A.

Abstract

This article examines the impact of serial correlation in high frequency returns on the realized variance measure. In particular, it is shown that the realized variance measure yields a biased estimate of the conditional return variance when returns are serially correlated. Using 10 years of FTSE-100 minute by minute data we demonstrate that a careful choice of sampling frequency is crucial in avoiding substantial biases. Moreover, we find that the autocovariance structure (magnitude and rate of decay) of FTSE-100 returns at different sampling frequencies is consistent with that of an ARMA process under temporal aggregation. A simple autocovariance function based method is proposed for choosing the “optimal” sampling frequency, that is, the highest available frequency at which the serial correlation of returns has a negligible impact on the realized variance measure. We find that the logarithmic realized variance series of the FTSE-100 index, constructed using an optimal sampling frequency of 25 minutes, can be modelled as an ARFIMA process. Exogenous variables such as lagged returns and contemporaneous trading volume appear to be highly significant regressors and are able to explain a large portion of the variation in daily realized variance.

Suggested Citation

  • Oomen, Roel C. A., 2004. "Modelling realized variance when returns are serially correlated [Modellierung realisierter Varianz bei autokorrelierten Erträgen]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2004-11, WZB Berlin Social Science Center.
    • Handle: RePEc:zbw:wzbmpg:spii200411
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    2. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    3. Daniel Djupsjobacka, 2010. "Implications of market microstructure for realized variance measurement," The European Journal of Finance, Taylor & Francis Journals, vol. 16(1), pages 27-43.
    4. Andrada-Félix, Julián & Fernández-Rodríguez, Fernando & Fuertes, Ana-Maria, 2016. "Combining nearest neighbor predictions and model-based predictions of realized variance: Does it pay?," International Journal of Forecasting, Elsevier, vol. 32(3), pages 695-715.
    5. Jian Zhou, 2017. "Forecasting REIT volatility with high-frequency data: a comparison of alternative methods," Applied Economics, Taylor & Francis Journals, vol. 49(26), pages 2590-2605, June.
    6. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    7. Konstantinos Gkillas & Christoforos Konstantatos & Costas Siriopoulos, 2021. "Uncertainty Due to Infectious Diseases and Stock–Bond Correlation," Econometrics, MDPI, vol. 9(2), pages 1-18, April.

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