Английская Википедия:Autoregressive conditional duration

Содержание

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Текст

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 <math> ~\tau_t~ </math> denote the duration (the waiting time between consecutive trades) and assume that <math> ~\tau_t=\theta_t z_t ~</math>, where <math> z_t </math> are independent and identically distributed random variables, positive and with <math> \operatorname{E}(z_t) = 1</math> and where the series <math> ~\theta_t~ </math> is given by:

<math> \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} </math>

and where <math> ~\alpha_0>0~ </math>, <math> \alpha_i\ge 0</math>, <math> \beta_i \ge 0 </math>, <math>~i>0</math>.

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.