Generalizing the Theta method for automatic forecasting Abstract   The Theta method became popular due to its superior performance in the M3 forecasting competition. Since then, although it has been shown that Theta provides accurate forecasts for various types of data, being a solid benchmark to beat, limited research has been conducted to exploit its full potential and generalize its reach. This paper examines three extensions on Thetaxe2x80x99s framework to boost its performance. This includes (i) considering both linear and nonlinear trends, (ii) allowing to adjust the slope of such trends, and (iii) introducing a multiplicative expression of the underlying forecasting model along with the existing, additive one. The proposed modifications transform Theta into a generalized forecasting algorithm, suitable for automatic time series predictions. The proposed algorithm is evaluated using the series of the M, M3, and M4 competitions. Such an evaluation shows that the proposed approach produces more accurate forecasts than the original, classic Theta, both in terms of point forecasts and prediction intervals, and is also more accurate than other wellknown methods for yearly series.

Studying the Performance of Cognitive Models in Time Series Forecasting Cognitive models have been paramount for modeling phenomena for which empirical data are unavailable, scarce, or only partially relevant. These approaches are based on methods dedicated to preparing experts and then to elicit their opinions about the variables that describe the phenomena under study. In time series forecasting exercises, elicitation processes seek to obtain accurate estimates, overcoming human heuristic biases, while being less time consuming. This paper aims to compare the performance of cognitive and mathematical time series predictors, regarding accuracy. The results are based on the comparison of predictors of the cognitive and mathematical models for several time series from the M3Competition. From the results, one can see that cognitive models are, at least, as accurate as ARIMA models predictions.