This paper proposes a new statistical model for the analysis of data which arrive at irregular intervals. The model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates. The conditional intensity is developed and compared with other self-exciting processes. Because the model focuses on the expected duration between events, it is called the autoregressive conditional duration (ACD) model. Asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to ARCH model results. Strong evidence is provided for duration clustering for the financial transaction data analyzed; both deterministic time-of-day effects and stochastic effects are important. The model is applied to the arrival times of trades and therefore is a model of transaction volume, and also to the arrival of other events such as price changes. Models for the volatility of prices are estimated with price-based durations, and examined from a market microstructure point of view.

A recent and extensive literature has pioneered the summing of squared observed intra-daily returns, "realized variance", to estimate the daily integrated variance of financial asset prices, a traditional object of economic interest. We show that, in the presence of market microstructure noise, realized variance does not identify the daily integrated variance of the frictionless equilibrium price. However, we demonstrate that the noise-induced bias at very high sampling frequencies can be appropriately traded off with the variance reduction obtained by high-frequency sampling and derive a mean-squared-error (MSE) optimal sampling theory for the purpose of integrated variance estimation. We show how our theory naturally leads to an identification procedure, which allows us to recover the moments of the unobserved noise; this procedure may be useful in other applications. Finally, using the profits obtained by option traders on the basis of alternative variance forecasts as our economic metric, we find that explicit optimization of realized variance's finite sample MSE properties results in accurate forecasts and considerable economic gains. Copyright 2008 The Review of Economic Studies Limited.

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