QPRC 2016

Multivariate count time series with long memory

Stefanos Kechagias

University of North Carolina

Abstract

In recent years, technological advancements in monitoring systems and data collection methods have motivated the use of multidimensional stochastic processes for simultaneous modeling of data originating from multiple sources. In contrast to the continuous time case, however, where vector autoregressive processes have a prominent role, no single class of discrete time processes has attracted similar attention. A possible reason for this is that existing multivariate discrete time series models are unable to produce arbitrary marginal distributions while allowing for negative auto and cross correlations. In this talk we introduce a multivariate count time series model that not only admits both of these traits but can also capture potential long memory behavior, a feature found in many real data sets in the form of a slowly decaying sample autocorrelation function. For the proposed model, we investigate the performance of an exact maximum likelihood estimation method through a Monte Carlo study and discuss other estimation approaches. This work is motivated by studying the frequency of hurricane occurrences,
using the number of major hurricanes observed in the North Atlantic and Pacific Ocean basins, where Poisson marginal distributions appear reasonable, negative autocorrelations are encountered, and long memory is present.