Non-linear prediction: a parsimonious family of predictors

The analysis of an observed univariate time series is often undertaken in order to get a prediction of a future event. With this purpose one can fix a class of predictors from which the optimal one will be identified and estimated. The more simple and common choice is the linear family, that is linear combinations of the lags of the series. However, it is well known that considering non-linearities in the lags may improve the prediction. We introduce in this paper a class of non-linear predictors based on polynomials and neural network methodology. These predictors have both the advantages of being relatively simple to identify and of introducing non-linearity without increasing the number of estimated parameters by much compared to linear predictors