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

Clive Bowsher
Nuffield College, University of Oxford, Oxford OX1 1NF, U.K.

Abstract:
A continuous time econometric modelling framework for multivariate
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. We introduce the class of generalised Hawkes models 
which allow the estimation of the dependence of the intensity on the events 
of previous trading days. Analytic likelihoods are available and we show how
to construct diagnostic tests based on the transformation of non-Poisson 
processes into standard Poisson processes using random changes of time scale.
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 NYSE stock and
the empirical findings are related to the theoretical and empirical market 
microstructure literature.
	
Keywords:  Point and counting processes, intensity, multivariate, diagnostics, 
goodness of fit, specification tests, change of timescale, transactions data, NYSE, 
NASDAQ, market microstructure