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

Presented by Norou Diawara, PhD

Professor of Statistics, Old Dominion University

Wednesday, Nov 1 2023
4:00 PM-5:00 PM ET
AUST 110
Webex Meeting Link

Count time series data have multiple applications. The applications can be found in areas of climate, public health, crime data analyses and more. 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. Besides the correlations, there is presence of zero- inflation in the data and dispersion. 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 talk, we propose two classes 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, zero-inflated negative binomial and zero-inflated Conway-Maxwell-Poisson marginals. Bivariate copula functions such as the bivariate Gaussian and t-copula are chosen to construct the distribution of consecutive observations.

In multivariate setting, 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 and conditional dependences with multiple lags. 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 great flexibility in modeling count time series data. To evaluate the superiority of both classes of models, simulated and real-life data examples are provided and studied.

Speaker Bio:

I am a Professor of Statistics in the Mathematics and Statistics Department at Old Dominion University (ODU), Norfolk, Virginia, United States. After a B.S. at the University Cheick Anta Diop in Dakar, Senegal, a Maîtrise in Mathematics at University of Le Havre, Le Havre, France, a Master’s in Mathematics and Statistics at University South Alabama, Mobile, Alabama, and a Ph.D. in Statistics from Auburn University in Auburn, Alabama in 2006, I took teaching position at ODU.
My research falls in Applied Statistics, and it can be classified into two main areas: (1) Spatio-temporal estimation methods and (2) Discrete choice modelling. It includes estimation of the spatio-temporal behaviors, estimation of time to event, and visualization of time series data. My research areas are in estimation techniques of time to event data analyses. Such research interests may be included in distributional functional, discrete choice models, statistical pattern recognition using copulas and spatial-temporal models. With the high volume of data, we bring analytic prospects in medical and engineering applications.