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Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model

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  • Siem Jan Koopman
  • Rutger Lit
  • André Lucas

Abstract

We study intraday stochastic volatility for four liquid stocks traded on the New York Stock Exchange using a new dynamic Skellam model for high-frequency tick-by-tick discrete price changes. Since the likelihood function is analytically intractable, we rely on numerical methods for its evaluation. Given the high number of observations per series per day (1000 to 10,000), we adopt computationally efficient methods including Monte Carlo integration. The intraday dynamics of volatility and the high number of trades without price impact require nontrivial adjustments to the basic dynamic Skellam model. In-sample residual diagnostics and goodness-of-fit statistics show that the final model provides a good fit to the data. An extensive day-to-day forecasting study of intraday volatility shows that the dynamic modified Skellam model provides accurate forecasts compared to alternative modeling approaches. Supplementary materials for this article are available online.

Suggested Citation

  • Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
  • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:520:p:1490-1503
    DOI: 10.1080/01621459.2017.1302878
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    3. Vladim'ir Hol'y & Petra Tomanov'a, 2021. "Modeling Price Clustering in High-Frequency Prices," Papers 2102.12112, arXiv.org, revised Mar 2021.
    4. Paolo Gorgi, 2020. "Beta–negative binomial auto‐regressions for modelling integer‐valued time series with extreme observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1325-1347, December.
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    6. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    7. Vladim'ir Hol'y, 2022. "An Intraday GARCH Model for Discrete Price Changes and Irregularly Spaced Observations," Papers 2211.12376, arXiv.org, revised Sep 2023.
    8. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    9. Matteo Iacopini & Carlo R.M.A. Santagiustina, 2021. "Filtering the intensity of public concern from social media count data with jumps," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1283-1302, October.
    10. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    11. Tobias Eckernkemper & Bastian Gribisch, 2021. "Intraday conditional value at risk: A periodic mixed‐frequency generalized autoregressive score approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 883-910, August.
    12. Harvey, A., 2021. "Score-driven time series models," Cambridge Working Papers in Economics 2133, Faculty of Economics, University of Cambridge.
    13. Koopman, Siem Jan & Lit, Rutger, 2019. "Forecasting football match results in national league competitions using score-driven time series models," International Journal of Forecasting, Elsevier, vol. 35(2), pages 797-809.
    14. Kung, Ko-Lun & Liu, I-Chien & Wang, Chou-Wen, 2021. "Modeling and pricing longevity derivatives using Skellam distribution," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 341-354.
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    16. Zhanyu Chen & Kai Zhang & Hongbiao Zhao, 2022. "A Skellam market model for loan prime rate options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 525-551, March.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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