Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models

Abstract

A continuous time econometric modelling framework for multivariate financial market event (or 'transactions') data is developed in which the model is specified via the vector stochastic intensity. This has the advantage that the conditioning sigma-field is updated continuously in time as new information arrives. The class of generalised Hawkes models is introduced which allows the estimation of the dependence of the intensity on the events of previous trading days. Analytic likelihoods are available and it is shown how to construct diagnostic tests based on the transformation of non-Poisson processes into standard Poisson processes using random changes of time. A proof of the validity of the diagnostic testing procedures is given that imposes only a very weak condition on the point process model, thus establishing their widespread applicability. A continuous time, bivariate point process model of the timing of trades and mid-quote changes is presented for a New York Stock Exchange stock and the empirical findings are related to the theoretical and empirical market microstructure literature. The two-way interaction of trades and quote changes is found to be important empirically.

Keywords: Point and counting processes, multivariate, intensity, Hawkes process, diagnostics, goodness-of-fit, specification tests, change of time, transactions data, NYSE, market microstructure

JEL Classification: C32, C51, C52, G10