Advancement of Autoregressive Conditional Duration Models involving Liquidity and Price Dynamics

Abstract

Financial market activity via trade durations and price dynamics are investigated by means of ultra high frequency data. Inter-trade arrival times of stock market trades are modelled by an Autoregressive Conditional Duration (ACD) model. Given the distinct features of financial duration data, conditional distribution of the ACD model has posed challenges to model parametrically. Problem under purview revolves around creating a sufficiently flexible parametric distribution to capture tail properties better than similar distributions in the existing ACD literature. Extending the idea, possibility of adequately modelling the full conditional distribution in better capturing of high near zero density and the heavy tail in financial trade durations, is explored. Furthermore, in terms of price dynamics, enhancing the predictive accuracy of one-step ahead forecasts while devising a mechanism to propel multi-step ahead forecasts of stock price movements are probed in detail within an ordered probit framework. An extended version of Weibull distribution is proposed first, as a new parametric error distribution for ACD model to counter the existing inadequacy of capturing the tail behaviour of trade durations. Designed with an extra shape parameter for greater flexibility, the properties of the proposed distribution are derived therein. A Bayesian estimator is developed and assessed through a simulation study. Empirical evidence of its performance based on two real life applications demonstrates robustness. To better represent the full conditional distribution, a mixture of two simple distributions is developed, recognising the heterogeneity in trader behaviour, which was then generalised. Based on empirical evidence, the generalised mixture distribution performs best in terms of model fit, while performing well in forecast and risk evaluation. Further, the dynamic nature of trading intensity is aptly captured by the time-varying mixture weights, which perform consistently better than the respective fixed weight counterparts. Forecast and extreme liquidity risk performance are assessed, where measures of extreme liquidity risk are based on extreme quantiles. Recognising the informational role of time on security price formation, the evolution of the price process is modelled via an ordered probit framework, which is employed to predict future price movements. Estimation and statistical inference is based on a maximum likelihood approach while a Bayesian estimator is developed for comparison. Discussed model provides improved forecast accuracy, against an existing study, while providing a benchmark for the 100-step ahead rolling forecasts. Furthermore, a new dimension is introduced with the aim of producing multi-step ahead forecasts, where individual explanatory variables are predicted a priori based on their serial correlation structures. This approach enhances flexibility and adaptability of the model to future price changes, targeting risk minimisation.