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

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.https://digitalcommons.odu.edu/gradposters2023_sciences/1026/thumbnail.jp

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models

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

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

Hierarchical Multiplicity Control Methods For Linear Models

HypoThesis testing is a commonly used statistical inference technique on which a statement of the population is investigated through the evidence from a representative sample of the population. With simultaneous testing of more than one null hypotheses need for an appropriate multiple comparison method is essential. With motivation from the study of Bogomolov et al. (2017) we have modified a multiple comparison tree structure to build the required comparisons and focus on controlling the FWER (Family Wise Error Rate) using the Bonferroni procedure. The proposed method has advantages such as controlling the global error rates separately at each level, families of hypotheses at high resolution are tested only when their parent hypotheses are rejected. In this study, a level restricted method is used to control the FWER at each level and a simulation study is performed to justify the proposed method. Additionally, the proposed method was applied to two real data sets in an educational setting to make multiple comparisons