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.