Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity

We propose a dynamic factor model for the analysis of multivariate time series count data. Our model allows for idiosyncratic as well as common serially correlated latent factors in order to account for potentially complex dynamic interdependence between series of counts. The model is estimated under alternative count distributions (Poisson and negative binomial). Maximum likelihood estimation requires high-dimensional numerical integration in order to marginalize the joint distribution with respect to the unobserved dynamic factors. We rely upon the Monte Carlo integration procedure known as efficient importance sampling, which produces fast and numerically accurate estimates of the likelihood function. The model is applied to time series data consisting of numbers of trades in 5-min intervals for five New York Stock Exchange (NYSE) stocks from two industrial sectors. The estimated model provides a good parsimonious representation of the contemporaneous correlation across the individual stocks and their serial correlation. It also provides strong evidence of a common factor, which we interpret as reflecting market-wide news.