# Copula Based Models for Bivariate Zero-Inflated Count Time Series Data

Summer 8-2023

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Mathematics & Statistics

## Program/Concentration

Computational and Applied Mathematics

Norou Diawara

Lucia Tabacu

Yet Nguyen

## Committee Member

Khan M. Iftekharuddin

## 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 most scenarios, time is an important part of the data. Time series counts then 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, and when a value, say zero, occurs more often than usual, analysis presents crucial challenges. There is presence of zeroinflation in the data. The literature on bivariate or multivariate count time series, as well as zero-inflated cases of time series, is limited due to the complexity of the computational burden in analyzing such data. In this dissertation, we propose two class of models to analyze bivariate count time series data in the presence of zero-inflation.

For the first class of models, we mainly focus on constructing bivariate Markov 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. We have considered 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 joint distribution of consecutive observations.

In multiple occasions, the pair copula construction shows that a particular structure (the R-vine) has the potential to capture the cross-sectional dependence in time series data. We propose a copula autoregressive (COPAR) model using Gaussian copula for such zero-inflated stationary time series with a Markovian structure. This second class of model captures both serial dependence and cross dependence in multivariate zero-inflated time series data. Further, our proposed class of models allows a general Markov structure which increases the flexibility of modeling count time series data. To evaluate the superiority of both class of models, simulated and real-life data examples are provided and studied.

## Rights

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## DOI

10.25777/8mtw-dr87

9798380393485