  We develop a novel observation-driven model for high-frequency prices. We
account for irregularly spaced observations, simultaneous transactions,
discreteness of prices, and market microstructure noise. The relation between
trade durations and price volatility, as well as intraday patterns of trade
durations and price volatility, is captured using smoothing splines. The
dynamic model is based on the zero-inflated Skellam distribution with
time-varying volatility in a score-driven framework. Market microstructure
noise is filtered by including a moving average component. The model is
estimated by the maximum likelihood method. In an empirical study of the IBM
stock, we demonstrate that the model provides a good fit to the data. Besides
modeling intraday volatility, it can also be used to measure daily realized
volatility.
