Parsimonious fuzzy time series modelling

Abstract

This paper proposes a novel modelling structure to ensure the parsimony of fuzzy time series (FTS) models while retaining certain level of out-of-sample accuracy. A parsimonious FTS model requires multiple optimizations of hyper-parameters such as time lags and partitioning which consists of the number of fuzzy sets, the partitioning type and the membership functions. In the vast literature of fuzzy time series, hyper-parameter optimization is usually ignored. In addition to that, optimization process for the hyper-parameters is also not presented properly. In this study, a parsimonious FTS modelling approach is introduced by using genetic algorithm (GA). Three major innovations are proposed: (1) Hyper-parameters of FTS structure are optimized to eliminate subjective preferences with the help of GA. Some of those parameters are never optimized or simply ignored in the past research. (2) The set of hyper-parameters is optimized subject to highest accuracy in validation set data and model’s complexity. (3) For achieving sparsification and accuracy simultaneously at reasonable computation time, a two-stage GA optimization is run to search for higher accuracy and lower complexity consecutively. Empirical studies are conducted on two types of datasets. Prices of liquid bulk cargo carriers (i.e. tanker) and secondhand ship have been predicted using the proposed approach. Potential benchmarks as well as a simple Nave forecast have been compared to the proposed model for validation based on mean absolute scaled error and root mean squared error.