Multivariate copula‐based integer‐valued time series models: theory and applications

Integer-valued time series comprising count observations at regular time intervals can be observed in various applications, such as the amount of crimes committed in a city per hour, the amount of insurance claims in a firm per year, the number of defaulted loans issued by a bank per week, the number of infected people per day, etc. Different time series can also be dependent on one another. This dependence can be described via a copula. In this thesis, a class of bivariate integer-valued autoregressive processes of order 1 (BINAR(1)) with copula-joint innovations are analysed. Model properties are derived and different parameter estimation methods are analysed. Estimation methods are compared via Monte Carlo simulation and an empirical application on loan default data is carried out. Integer-valued time series can also exhibit seasonal fluctuations. A univariate integer-valued autoregressive process for seasonality with period d (SINAR(1)_d) is introduced in this thesis, which allows for intra-seasonal dependence of the innovations to be described by a copula. Such a univariate process can also be written as a multivariate specification. Model properties are derived. Parameter estimation methods are analysed and compared via Monte Carlo simulation. An empirical application on Chicago crime data is carried out