Analysis of Financial Time Series, Third Edition

5.5 Duration Models

Duration models are concerned with time intervals between trades. Longer durations indicate lack of trading activities, which in turn signify a period of no new information. The dynamic behavior of durations thus contains useful information about intraday market activities. Using concepts similar to the ARCH models for volatility, Engle and Russell (1998) propose an autoregressive conditional duration (ACD) model to describe the evolution of time durations for (heavily traded) stocks. Zhang et al. (2001) extend the ACD model to account for nonlinearity and structural breaks in the data. In this section, we introduce some simple duration models. As mentioned before, intraday transactions exhibit some diurnal pattern. Therefore, we focus on the adjusted time duration

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where f(ti) is a deterministic function consisting of the cyclical component of Δti. Obviously, f(ti) depends on the underlying asset and the systematic behavior of the market. In practice, there are many ways to estimate f(ti), but no single method dominates the others in terms of statistical properties. A common approach is to use smoothing spline. Here we use simple quadratic functions and indicator variables to take care of the deterministic component of daily trading activities.

For the IBM data employed in the illustration of ADS models, we assume

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where

and f5(ti) and f6(ti) are indicator ...