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Koopman, Siem Jan
Lit, Rutger
Lucas, Andre
Year of Publication: 
Series/Report no.: 
Tinbergen Institute Discussion Paper 15-076/IV/DSF94
We introduce a dynamic Skellam model that measures stochastic volatility from high-frequency tick-by-tick discrete stock price changes. The likelihood function for our model is analytically intractable and requires Monte Carlo integration methods for its numerical evaluation. The proposed methodology is applied to tick-by-tick data of four stocks traded on the New York Stock Exchange. We require fast simulation methods for likelihood evaluation since the number of observations per series per day varies from 1000 to 10,000. Complexities in the intraday dynamics of volatility and in the frequency of trades without price impact require further non-trivial adjustments to the 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 forecasting study of intraday volatility shows that the dynamic modified Skellam model provides accurate forecasts compared to alternative modeling approaches.
non-Gaussian time series models
volatility models
importance sampling
numerical integration
high-frequency data
discrete price changes.
Document Type: 
Working Paper

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