Recursive and direct multi-step forecasting: the best of both worlds

Souhaib Ben Taieb, Rob J Hyndman


We propose a new forecasting strategy, called rectify, that seeks to combine the best properties of both the recursive and direct forecasting strategies. The rationale behind the rectify strategy is to begin with biased recursive forecasts and adjust them so they are unbiased and have smaller error. We use linear and nonlinear simulated time series to investigate the performance of the rectify strategy and compare the results with those from the recursive and the direct strategies. We also carry out some experiments using real world time series from the M3 and the NN5 forecasting competitions. We find that the rectify strategy is always better than, or at least has comparable performance to, the best of the recursive and the direct strategies. This finding makes the rectify strategy very attractive as it avoids making a choice between the recursive and the direct strategies which can be a difficult task in real-world applications.