Prediction interval for long financial series

This paper develops a method of modelling that may be applied to build approximated prediction intervals for long series with heteroscedastic conditional variance. The first step of modelling is represented by the estimation of the values of the series, given a vector of exogenous or lagged endogenous variables, by means of a flexible non-linear function in which the parameters are selected with the minimisation of the weight-decay cost function. The second step is represented by the estimation of the conditional variance associated with each prediction, through a second non-linear function in which the target values are given by the squared errors obtained in the first step. An application on 4 financial index series illustrates the method and shows its good forecasting ability.