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

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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.

Original languageEnglish
Pages (from-to)1490-1503
Number of pages14
JournalJournal of the American Statistical Association
Issue number520
Publication statusPublished - 2017


Lit and Lucas acknowledge the financial support of the Dutch National Science Foundation (NWO grant VICI453-09-005). Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation, (DNRF78).

FundersFunder number
Aarhus Universitet
Danmarks GrundforskningsfondDNRF78
Nederlandse Organisatie voor Wetenschappelijk OnderzoekVICI453-09-005


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