Time Series Complexities and Their Relationship to Forecasting Performance Entropy is a key concept in the characterization of uncertainty for any given signal, and its extensions such as Spectral Entropy and Permutation Entropy. They have been used to measure the complexity of time series. However, these measures are subject to the discretization employed to study the states of the system, and identifying the relationship between complexity measures and the expected performance of the four selected forecasting methods that participate in the M4 Competition. This relationship allows the decision, in advance, of which algorithm is adequate. Therefore, in this paper, we found the relationships between entropybased complexity framework and the forecasting error of four selected methods (Smyl, Theta, ARIMA, and ETS). Moreover, we present a framework extension based on the Emergence, SelfOrganization, and Complexity paradigm. The experimentation with both synthetic and M4 Competition time series show that the feature space induced by complexities, visually constrains the forecasting method performance to specific regions; where the logarithm of its metric error is poorer, the Complexity based on the emergence and selforganization is maximal.

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.