Yuvraj Sunecher

Modelling a non-stationary BINAR(1) Poisson process

ABSTRACT Non-stationarity in bivariate time series of counts may be induced by a number of time-varying covariates affecting the bivariate responses due to which the innovation terms of the individual series as well as the bivariate dependence structure becomes non-stationary. So far, in the existing models, the innovation terms of individual INAR(1) series and the dependence structure are assumed to be constant even though the individual time series are non-stationary. Under this assumption, the reliability of the regression and correlation estimates is questionable. Besides, the existing estimation methodologies such as the conditional maximum likelihood (CMLE) and the composite likelihood estimation are computationally intensive. To address these issues, this paper proposes a BINAR(1) model where the innovation series follow a bivariate Poisson distribution under some non-stationary distributional assumptions. The method of generalized quasi-likelihood (GQL) is used to estimate the regression effects while the serial and bivariate correlations are estimated using a robust moment estimation technique. The application of model and estimation method is made in the simulated data. The GQL method is also compared with the CMLE, generalized method of moments (GMM) and generalized estimating equation (GEE) approaches where through simulation studies, it is shown that GQL yields more efficient estimates than GMM and equally or slightly more efficient estimates than CMLE and GEE.

Estimating the parameters of a BINMA Poisson model for a non-stationary bivariate time series

ABSTRACT This article proposes a novel non-stationary BINMA time series model by extending two INMA processes where their innovation series follow the bivariate Poisson under time-varying moment assumptions. This article also demonstrates, through simulation studies, the use and superiority of the generalized quasi-likelihood (GQL) approach to estimate the regression effects, which is computationally less complicated as compared to conditional maximum likelihood estimation (CMLE) and the feasible generalized least squares (FGLS). The serial and bivariate dependence correlations are estimated by a robust method of moments.

A GQL estimation approach for analysing non-stationary over-dispersed BINAR(1) time series

ABSTRACT This paper proposes a generalized quasi-likelihood (GQL) function for estimating the vector of regression and over-dispersion effects for the respective series in the bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with Negative Binomial (NB) marginals. The auto-covariance function in the proposed GQL is computed using some ‘robust’ working structures. As for the BINAR(1) process, the inter-relation between the series is induced mainly by the correlated NB innovations that are subject to different levels of over-dispersion. The performance of the GQL approach is tested via some Monte-Carlo simulations under different combination of over-dispersion together with low and high serial- and cross-correlation parameters. The model is also applied to analyse a real-life series of day and night accidents in Mauritius.

Inferential methods for an unconstrained nonstationary BINMA time series process with Poisson innovations

This article proposes an unconstrained nonstationary BINMA(l) time-series process with Poisson innovations under time-dependent moments where the cross-correlation structure is formed firstly by the jointly distributed innovations and second by relating the current varíate observations with the previous lagged innovation of the other series and vice versa. For this new BINMA(1) time series model, feasible generalized least squares (FGLS), generalized method of moments (GMM), and generalized quasi-likelihood (GQL) estimating equations are developed. A simulation process is set up to generate BINMA(l) time-series data under the unconstrained cross-correlation structure. The purpose here is to assess the performance of the different estimation techniques proposed. The article also analyzes real-life monthly day and night accidents data in Mauritius under this model.

A BINAR(1) Time Series Model with Cross-Correlated COM-Poisson Innovations

ABSTRACT This article proposes a bivariate integer-valued autoregressive time-series model of order 1 (BINAR(1) with COM–Poisson marginals to analyze a pair of non stationary time series of counts. The interrelation between the series is induced by the correlated innovations, while the non stationarity is captured through a common set of time-dependent covariates that influence the count responses. The regression and dependence effects are estimated using generalized quasi-likelihood (GQL) approach. Simulation experiments are performed to assess the performance of the estimation algorithms. The proposed BINAR(1) process is applied to analyze a real-life series of day and night accidents in Mauritius.

A non-stationary BINAR(1) process with negative binomial innovations for modeling the number of goals in the first and second half: The case of Arsenal Football Club

ABSTRACT Arsenal Football Club has been among the top four in the Premier League for long, but recently the clubs performance has been quite inconsistent. This article performs a regression analysis to determine the factors that could explain these inconsistencies using a simple non-stationary first-order bivariate integer-valued autoregressive process with negative binomial cross-correlated innovations (BINAR(1)NB). The estimation of parameters is performed using a generalized quasi-likelihood approach. A small simulation study is presented. The BINAR(1)NB is also compared with other bivariate time series models.

Communication in Statistics-Theory and methods improved GQL estimation method for the generalised BINMA(1) model

ABSTRACT In a recent research, the quasi-likelihood estimation methodology was developed to estimate the regression effects in the Generalized BINMA(1) (GBINMA(1)) process. The method provides consistent parameter estimates but, in the intermediate computations, moment estimating equations were used to estimate the serial- and cross-correlation parameters. This procedure may not result optimal parameter estimates, in particular, for the regression effects. This paper provides an alternative simpler GBINMA(1) process based on multivariate thinning properties where the main effects are estimated via a robust generalized quasi-likelihood (GQL) estimation approach. The two techniques are compared through some simulation experiments. A real-life data application is studied.

A Flexible Observation-Driven Stationary Bivariate Negative Binomial INAR(1) with Non-homogeneous Levels of Over-dispersion

Abstract The existing bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with negative binomial (NB) innovations is developed under stationary moment conditions and in particular under same level of over-dispersion index. In this paper, we propose a flexible BINAR(1) under NB innovations where the counting series are subject to two different levels of over-dispersion under same stationary moment condition. The unknown parameters of the new model are estimated using a generalized quasi-likelihood (QL) estimating equation. The performance of this estimation method is assessed through some numerical experiments under different time dimensions.

A case study of MCB and SBMH stock transaction using a novel BINMA(1) with non-stationary NB correlated innovations

ABSTRACT This paper focuses on the modeling of the intra-day transactions at the Stock Exchange Mauritius (SEM) of the two major banking companies: Mauritius Commercial Bank Group Limited (MCB) and State Bank of Mauritius Holdings Ltd (SBMH) in Mauritius using a flexible non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) process with negative binomial (NB) innovations that may cater for different levels of over-dispersion. The generalized quasi-likelihood (GQL) approach is used to estimate the regression, dependence and over-dispersion effects. However, for the over-dispersion parameters, the auto-covariance structure in the GQL is constructed using some higher order moments. This new model is tested over some Monte-Carlo experiments and is applied to analyze the inter-related intra-day series of volume of stocks for the two banking institutions using data collected from 3 August to 16 October 2015 in the presence of some time-varying covariates such as the news effect, Friday effect and time of the day effect.

Estimation Methods for a Flexible INAR(1) COM-Poisson Time Series Model

Abstract Time series of counts occur in many real-life situations where they exhibit various forms of dispersion. To facilitate the modeling of such time series, this paper introduces a flexible first-order integer-valued non-stationary autoregressive (INAR(1)) process where the innovation terms follow a Conway-Maxwell Poisson distribution (COM-Poisson). To estimate the unknown parameters in this model, different estimation approaches based on likelihood and quasi-likelihood formulations are considered. From simulation experiments and a real-life data application, the Generalized Quasi-Likelihood (GQL) approach yields estimates with lower bias than the other estimation approaches.