A distribution-free method for forecasting non-gaussian time series

The non-linear instantaneous transformation is a method to model and forecast non-Gaussian time series. A restriction of this method is that the marginal distribution of data must be known, or a general distribution form has to be determined. A difficulty of this method is that in practice the distribution of observed data is usually unknown, and it needs to be determined by fitting the data. In this study, a distribution-free plotting position formula is applied to the non-linear instantaneous transformation method. Synthetic time series and observed data are used to illustrate the proposed method, which does not require fitting the marginal distribution of the data to be forecasted.