Semi-parametric time series modelling with autocopulas

In this paper we present an application of the use of autocopulas for modelling financial time series showing serial dependencies that are not necessarily linear. The approach presented here is semi-parametric in that it is characterized by a non-parametric autocopula and parametric marginals. One advantage of using autocopulas is that they provide a general representation of the auto-dependency of the time series, in particular making it possible to study the interdependence of values of the series at different extremes separately. The specific time series that is studied here comes from daily cash flows involving the product of daily natural gas price and daily temperature deviations from normal levels. Seasonality is captured by using a time dependent normal inverse Gaussian (NIG) distribution fitted to the raw values.