Integer-valued time series data naturally occurs in various areas whenever a number of events are observed over time. The model considered in this study consists of a Gaussian copula with autoregressive-moving average (ARMA) dependence and discrete margins that can be specified, unspecified, with or without covariates. It can be interpreted as a ‘digitised’ ARMA model. An ARMA model is used for the latent process so that well-established methods in time series analysis can be used.

Still the computation of the log-likelihood poses many problems because it is the sum of 2^n terms involving the Gaussian cumulative distribution function when n is the length of the time series.

We consider three estimation methods for the Gaussian copula model applied to integer-valued time series.

Supervised by: Dr Jingsong Yuan