Analyzing Stock Series Data Via Classes of Non-Stationary Integer-Valued Bivariate Auto-Regressive Time Series Models

Time series of counts commonly arise in fields of finance, transport, education, health and among many others. In such application areas, there exists di_erent variables of interest that may exhibit some inter-relationships. For example, day and night accidents for a one-year period over a particular motorway will surely exhibit some cross correlation while the volume of transactions of competing companies in the shares market are influential to each other such as the case of AstraZeneca and Ericsson B in the Swedish stock exchange. Such series of data impose some significant challenges: Firstly, these series of counts display some serial auto-correlation structures while simultaneously indicating some significant cross correlation. On the other hand, the counting series are influenced by several time-dependent factors which induce non-stationary moments. Basically, the observations in these series also express huge variability In this paper, we propose three different classes of bivariate integer-valued auto-regressive models of order 1 (BINAR (1)) to model such types of series. For simplicity, we assume that the innovation terms follow the Geometric model such that to account for the over-dispersion features. As for the inferential procedures, the conditional maximum likelihood (CML) approach is used to estimate the different models parameters. Some Monte Carlo numerical experiments are executed to assess the performance of CML and an application to the AstraZeneca and Erricsson B data is illustrated. Keywords - Time Series, Counts, Bivariate, Geometric, CML