Yet Another ACD Model: The Autoregressive Conditional Directional Duration (ACDD) Model

This paper features a new autoregressive conditional duration (ACD) model which sits within the theoretical framework provided by the recently developed observation-driven time series models by Creal et al. (2013): the generalized autoregressive score (GAS) models. The autoregressive conditional directional duration (ACDD) model itself contains three novelties. First, durations (intra-trade intervals or waiting-times) are signed, based on whether a (positive) ask-driven trade or a (negative) bid-driven trade occurred. These signed trade-durations are known as directional durations. Second, as the resultant directional durations are no longer positive and asymmetrical but are symmetrically distributed, the familiar generalized autoregressive conditional heteroskedasticity (GARCH)-like formulation of the ACD process is proposed for modeling these directional durations. Consequently, the proposed model is called the ACDD model. Third, using the alternative GARCH-like formulation, persistence or long-memory in the durations is easily addressed both via the mean and variance equations: the mean equation uses a semi-parametric fractional autoregressive (SEMIFAR) formulation and the variance equation uses a GARCH formulation. The paper demonstrates the flexibility and convenience of the generalized autoregressive score (GAS) model framework in the context of a particular ACD model specification. The model can be viewed as an alternative extension of the “asymmetric ACD model” of Bauwens and Giot (2003) which captures information related to the evolution of prices as well as the quote-durations.