Non‐monotonic hazard functions and the autoregressive conditional duration model

Abstract

This paper shows that the monotonicity of the conditional hazard in traditional ACD models is both econometrically important and empirically invalid. To counter this problem we introduce a more flexible parametric model which is easy to fit and performs well both in simulation studies and in practice. In an empirical application to NYSE price duration processes, we show that non-monotonic conditional hazard functions are indicated for all stocks. Recently proposed specification tests for financial duration models clearly reject the standard ACD models, whereas the results for the new model are quite favorable.

Dynamic Latent Factor Models for Intensity Processes

“…Since the introduction of the autoregressive conditional duration (ACD) model proposed by Engle and Russell (1998) and Engle (2000), much research has been devoted to the specification and application of discrete time autoregressive duration models (see Bauwens and Giot, 2000, Grammig and Maurer, 2000, Dufour and Engle, 2000, Fernandes and Grammig, 2001, and Hautsch, 2002. An obvious reason for the focus on duration models is that the inclusion of dynamic structures, which is essential for modelling financial point processes, is quite straightforward.…”

The logarithmic ACD model: The microstructure of the German and Polish stock markets

“…Gramming and Maurer (2000) derived an ACD model based on the Burr distribution (an alternative to the Weibull distribution). Jasiak (1998) extended ACD to the fractionally integrated ACD model.…”

Trade intensity in the Russian stock market: dynamics, distribution and determinants

“…Engle and Russell (1998) used the exponential and Weibull distributions. These choices, however, imply an unrealistic monotonic conditional hazard function, which led Lunde (1999) to propose the generalized gamma distribution, and Grammig and Maurer (2000) the more exotic Burr distribution. When the density is specified, one can proceed with the maximum likelihood (ML) estimation.…”

“…Grammig and Maurer (2000) come to the conclusion that allowing for non-monotonic hazard functions is an important issue in modeling durations. Even in a conditionally normal homoscedastic Log-ARMA model, the conditional distribution of durations is lognormal and thus the conditional hazard function is non-monotonic, increasing for small durations and decreasing for larger durations, which is consistent with estimated patterns (e.g., Grammig and Maurer, 2000, Figure 5).…”