# 15-076/IV/DSF94 (2015-07-01)

Siem Jan Koopman, VU University Amsterdam; Rutger Lit, VU University Amsterdam; Andre Lucas, VU University Amsterdam
non-Gaussian time series models; volatility models; importance sampling; numerical integration; high-frequency data; discrete price changes.
JEL codes:
C22, C32, C58

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.