A Flexible Stochastic Conditional Duration Model

Abstract

We introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any two trades executed in the same second are probably related, it is extremely unlikely that all such pairs of trades are, in a typical sample.By placing uncertainty about which trades are related within our model, we improve inference for the distribution of durations between unrelated trades, especially near zero. We introduce a normalized conditional distribution for durations between unrelated trades that is both flexible and amenable to shrinkage towards an exponential distribution, which we argue is an appropriate first-order model. Thanks to highly efficient draws of state variables, numerical efficiency of posterior simulation is much higher than in previous studies. In an empirical application, we find that the conditional hazard function for durations between unrelated trades varies much less than what most studies find. We claim that this is because we avoid statistical artifacts that arise from deterministic trade-aggregation rules and unsuitable parametric distributions.

Stochastic Conditional Duration Model with Intraday Seasonality and Limit Order Book Information

“…To imply the intraday seasonality by the model, we follow Eilers and Marx (1996), Lang and Brezger (2004), Brownlees and Vannucci (2013) and Gingras and McCausland (2020) and use the B-Spline in the observation equation. B-Spline is a piecewise polynomial function driven by control points.…”

“…The model assumes that the AR(1) process switches between the two regimes, allowing us to consider the behavior of two types of traders with different behavioral criteria. Gingras and McCausland (2020) proposed the all-duration flexible SCD (FSCD) model. This is an extension of the SCD model that attempts to model transactions occurring at the same second with a mixture distribution and uses the B-Spline to capture intraday seasonality.…”