Error modeling approach to improve time series forecasters

In time series forecasting exercises it has been usual to suppose that the error series generated by the forecasters have a white noise behavior. However, it is possible that such supposition is violated in practice due to model misspecification or disturbances of the phenomenon not captured by the predictive models. It may lead to statistically biased and/or inefficient predictors. The present paper introduces an approach to correct predetermined forecasters by recursively modeling their remaining residuals. Two formalisms are used to illustrate the recursive approach: the well-known (linear) autoregressive integrated moving average (ARIMA) and the (non-linear) Artificial Neural Network (ANN). These models are recursively adjusted to the remaining residuals of a given forecaster until a white noise behavior is achieved. Applications involving ARIMA and ANN forecasters for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, Nasdaq Index, Wolf׳s Sunspot, and Canadian Lynx data series indicate the usefulness of the proposed framework.