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We develop a novel observation-driven model for high-frequency prices. Weaccount for irregularly spaced observations, simultaneous transactions,discreteness of prices, and market microstructure noise. The relation betweentrade durations and price volatility, as well as intraday patterns of tradedurations and price volatility, is captured using smoothing splines. Thedynamic model is based on the zero-inflated Skellam distribution withtime-varying volatility in a score-driven framework. Market microstructurenoise is filtered by including a moving average component. The model isestimated by the maximum likelihood method. In an empirical study of the IBMstock, we demonstrate that the model provides a good fit to the data. Besidesmodeling intraday volatility, it can also be used to measure daily realizedvolatility.

An Intraday GARCH Model for Discrete Price Changes and Irregularly Spaced Observations