Title: An improved method of combining forecasts based on fourth cumulant
Authors: Massimiliano Giacalone - University of Naples - Federico II (Italy) [presenting]
Raffaele Mattera - University of Naples Federico II (Italy)
Abstract: A well-known result in statistics and econometrics is that a linear combination of two point forecasts has a smaller Mean Square Error (MSE) than the two competing forecasts themselves. The kind of combination methods are various, ranging from the simple average (SA) to more robust methods as the one based on median or on a Trimmed Average (TA) to other methods based on regression or optimization techniques. Using the regression-based approach, the resulting combined forecast is a linear function of the individual forecasts where the weights are estimated via Ordinary Least Squares (OLS), minimizing the sum of squared errors. A clear advantage of the OLS forecast combination method is that the combined resulting forecast is unbiased even if one of the individual forecasts is biased. Other alternative methods were developed, implementing the minimization of a different loss function, as happen with the least absolute sum of squares. However, these methods may fail to get a realistic result if the forecasts density are heavy-tailed, as happen in many situation (e.g. financial time series). Therefore, we propose a forecast combination method based on Lp-norm estimator, where the minimization of residuals is done according to estimated data kurtosis and the selection of more relevant forecast is achieved via a projection pursuit based on fourth cumulant. A simulation study is presented in order to show improvements in forecasting accuracy.