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Autoregressive conditional duration

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In financial econometrics, an autoregressive conditional duration (ACD, Engle and Russell (1998)) model considers irregularly spaced and autocorrelated intertrade durations. ACD is analogous to GARCH. In a continuous double auction (a common trading mechanism in many financial markets) waiting times between two consecutive trades vary at random.

Definition

Let   τ t   {\displaystyle ~\tau _{t}~} denote the duration (the waiting time between consecutive trades) and assume that   τ t = θ t z t   {\displaystyle ~\tau _{t}=\theta _{t}z_{t}~} , where z t {\displaystyle z_{t}} are independent and identically distributed random variables, positive and with E ⁡ ( z t ) = 1 {\displaystyle \operatorname {E} (z_{t})=1} and where the series   θ t   {\displaystyle ~\theta _{t}~} is given by:

θ t = α 0 + α 1 τ t − 1 + ⋯ + α q τ t − q + β 1 θ t − 1 + ⋯ + β p θ t − p = α 0 + ∑ i = 1 q α i τ t − i + ∑ i = 1 p β i θ t − i {\displaystyle \theta _{t}=\alpha _{0}+\alpha _{1}\tau _{t-1}+\cdots +\alpha _{q}\tau _{t-q}+\beta _{1}\theta _{t-1}+\cdots +\beta _{p}\theta _{t-p}=\alpha _{0}+\sum _{i=1}^{q}\alpha _{i}\tau _{t-i}+\sum _{i=1}^{p}\beta _{i}\theta _{t-i}}

and where   α 0 > 0   {\displaystyle ~\alpha _{0}>0~} , α i ≥ 0 {\displaystyle \alpha _{i}\geq 0} , β i ≥ 0 {\displaystyle \beta _{i}\geq 0} ,   i > 0 {\displaystyle ~i>0} .

References

  • Robert F. Engle and J.R. Russell. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data", Econometrica, 66:1127-1162, 1998.
  • N. Hautsch. "Modelling Irregularly Spaced Financial Data", Springer, 2004.
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