Combining forecasts is a common practice in time series analysis. This technique involves weighing each estimate of different models in order to minimize the error between the resulting output and the target. This work presents a novel methodology, aiming to combine forecasts using genetic programming, a metaheuristic that searches for a nonlinear combination and selection of forecasters simultaneously. To present the method, the authors made three different tests comparing with the linear forecasting combination, evaluating both in terms of RMSE and MAPE. The statistical analysis shows that the genetic programming combination outperforms the linear combination in two of the three tests evaluated.
In time series analysis, aiming in univariate forecasting, we can find several approaches traditionally focusing on mathematical and statistical methods (Atsalakis & Valavanis, 2009; Stepnicka et al., 2013). In this way, forecasting models like naive, linear and nonlinear models and Holt-Winters (Hyndman et al., 2008; Taylor, 2012) are mathematical methods that use extracted components (trend, seasonality, etc.) or past samples of the underlying process as a way to produce forecasts. Although, a time series can also be understood as a stochastic process that follows a specific probability distribution. By this principle, regression analysis and autoregressive integrated with moving average (ARIMA) models (Box et al., 1994; Valenzuela et al., 2008) are adequate tools that provide good performance if the time series follows all the statistical assumptions, for example, the time series follows a Gaussian distribution.