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Modeling discontinuous periodic conditional volatility: Evidence from the commodity futures market

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  • Nicholas Taylor

Abstract

This paper examines a wide variety of models that allow for complex and discontinuous periodic variation in conditional volatility. The value of these models (including augmented versions of existing models) is demonstrated with an application to high frequency commodity futures return data. Their use is necessary, in this context, because commodity futures returns exhibit discontinuous intraday and interday periodicities in conditional volatility. The former of these effects is well documented for various asset returns; however, the latter is unique amongst commodity futures returns, where contract delivery and climate are driving forces. Using six years of high‐frequency cocoa futures data, the results show that these characteristics of conditional return volatility are most adequately captured by a spline‐version of the periodic generalized autoregressive conditional heteroscedastic (PGARCH) model. This model also provides superior forecasts of future return volatility that are robust to variation in the loss function assumed by the user, and are shown to be beneficial to users of Value‐at‐Risk (VaR) models. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:805–834, 2004

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  • Nicholas Taylor, 2004. "Modeling discontinuous periodic conditional volatility: Evidence from the commodity futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(9), pages 805-834, September.
    • Handle: RePEc:wly:jfutmk:v:24:y:2004:i:9:p:805-834
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    Cited by:

    1. Abdelhakim Aknouche & Eid Al-Eid, 2012. "Asymptotic inference of unstable periodic ARCH processes," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 61-79, April.
    2. Sobhesh Kumar Agarwalla & Ajay Pandey, 2013. "Expiration‐Day Effects and the Impact of Short Trading Breaks on Intraday Volatility: Evidence from the Indian Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(11), pages 1046-1070, November.
    3. B.B. Chakrabarti & Vivek Rajvanshi, 2017. "Intraday Periodicity and Volatility Forecasting: Evidence from Indian Crude Oil Futures Market," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 16(1), pages 1-28, April.
    4. Agarwalla, Sobhesh Kumar & Pandey, Ajay, 2012. "Whether Cross-Listing, Stock-specific and Market-wide Calendar Events impact Intraday Volatility Dynamics? Evidence from the Indian Stock Market using High-frequency Data," IIMA Working Papers WP2012-11-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Abdelhakim Aknouche & Abdelouahab Bibi, 2009. "Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 19-46, January.
    6. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
    7. Xu, Kewei & Xiong, Xiong & Li, Xiao, 2021. "The maturity effect of stock index futures: Speculation or carry arbitrage?," Research in International Business and Finance, Elsevier, vol. 58(C).
    8. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.

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