THE NON-STATIONARY BIVARIATE INAR UNDER AN UNCONSTRAINED INTER CORRELATION STRUCTURE

Abstract

It is commonly observed in medical and financial studies that large volume of time series
of count data are collected for several variates. The modelling of such time series and
the estimation of parameters under such processes are rather challenging since these high
dimensional time series are influenced by time-varying covariates that eventually render
the data non-stationary. This paper considers the modelling of a bivariate integer-valued
autoregressive (BINAR(1)) process where the innovation terms are distributed under nonstationary
Poisson moments. Since the full and conditional likelihood approaches are cumbersome
in this situation, a Generalized Quasi-likelihood (GQL) approach is proposed to
estimate the regression effects while the serial and time-dependent cross correlation effects
are handled by method of moments. This new technique is assessed over several simulation
experiments and the results demonstrate that GQL yields consistent estimates and is
computationally stable since few non-convergent simulations are reported.