Modelling and forecasting time series with a general non-normal distribution

This paper proposes a model for time series with a general marginal distribution given by the Johnson family of distributions. It investigates for which Johnson distributions forecasting using the model is likely to be most effective compared to using a linear model. Monte Carlo simulation is used to assess the reliability of methods for determining which of the three Johnson forms is most appropriate for a given series. Finally, the paper gives model fitting and forecasting results using the modelling procedure on a selection of simulated and real time series.