Copula-Based Models for Bivariate and Multivariate Zero-inflated Count Time Series Data

Abstract

Count time series data have multiple applications. The applications can be found in areas of finance, climate, public health and crime data analyses. In some scenarios, count time series come as multivariate vectors that exhibit not only serial dependence within each time series but also with cross correlation among the series. When considering these observed counts, analysis presents crucial challenges when a value, say zero, occurs more often than usual. There is presence of zero-inflation in the data. In this presentation, we mainly focus on modeling bivariate zero-inflated count time series model based on a joint distribution of the two consecutive observations. The bivariate zero-inflated models are constructed through copula functions. Such Gaussian copula can accommodate both serial dependence and cross-sectional dependence in zero-inflated count time series data. We consider the first order Markov chains with zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) and zero-inflated Conway-Maxwell-Poisson (ZICMP) marginals. Bivariate copula functions such as the bivariate Gaussian and t-copula are chosen to construct the distribution of consecutive observations. Likelihood based inference is used to estimate the model parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized importance sampling method. To evaluate the superiority of the model, simulated (under positive and negative cross-correlations) are provided and presented. Real data examples are also shared. Extensions for high dimensional scenarios are discussed by introducing the copula autoregressive model (COPAR) with pair copula construction and vine tree structure. Structure matrices of the COPAR of orders 1 and 2 are shown. Simulations are conducted to validate the models.