Extension to a fuzzy cognitive maps-based approach for modelling granular time series for forecasting tasks

Abstract

Time series modeling for forecasting tasks is a complex problem of great interest to the scientific community. Most forecasting techniques are performed point by point. An alternative is to approximate time series with a higher-level (granular) representation, such that instead of forecasting numerical time series, the objective is to model and forecast at the granularity of the information. In this study, we propose a new approach for granular modeling of time series using Fuzzy Cognitive Maps (FCM). This approach builds on a previous approach that proposes time-segment granulation, which is then fuzzily clustered into clusters. Then, the cluster centroids are used as concepts in the fuzzy cognitive map (FCM) to define a time-series forecasting model. Specifically, we propose three improvements: (i) to the membership function for obtaining the clusters, (ii) to the optimization algorithm for obtaining the FCM, and (iii) to the function it uses to perform the forecast. Tests were carried out with time series of different types, for both granular and numerical forecasts. The experiments carried out demonstrate the robustness of the proposed approach in time series of different characteristics (time series with trends, stationarity, and seasonality). The approach introduced in the paper consistently outperforms the original approach and classical methods such as ARIMA. Overall, our granular approach is very effective at capturing the complexity of non-linear or abruptly changing series, as well as non-stationary and complex patterns.