Forecasting Seasonal Time Series with Multilayer Perceptrons - An Empirical Evaluation of Input Vector Specifications for Deterministic Seasonality

Research in forecasting with Neural Networks (NN) has provided contradictory evidence on their ability to model seasonal time series. Several empirical studies have concluded that time series should be deseasonalised prior to modelling, with contradictory evidence pointing to adequate selection of input vectors. However, the nature of seasonality itself has not been considered: econometric theory suggests that deterministic seasonality and stochastic seasonality need to be modelled differently, with only the latter requiring deseasonalisation. As prior research has failed to take the conditions of the underlying seasonality into consideration, this study explores how deterministic seasonality should be best modelled with NN to achieve accurate and robust forecasts. We consider different forms of modelling seasonality as autoregressive lags, through different encodings of explanatory variables and deseasonalisation. We evaluate the results regarding empirical accuracy and the parsimony of the input vector in order to limit the degrees of freedom, develop robust models and simplify the training of NN. Our findings are consistent with econometric literature, i.e. that no deseasonalisation is required for deterministic seasonality, and contributes to current research in NNs by identifying a more parsimonious coding of seasonality based on seasonal indices.