A Firefly Optimization Algorithm for Forecasting Based on Time-Variant Fuzzy Time Series

Forecasting has always been a crucial challenge for managers and scientists in terms of making accurate management or investment decisions. Although there are a variety of time series models in the literature, fuzzy time series modelling has attracted attention over the past decade to improve forecast accuracy with a small sample of data. This paper aims to present a fuzzy time series methodology for forecasting exchange rate trends that could serve as a scientific approach toward feasible and sustainable economic development policies. Specifically, we propose a hybrid algorithm to deal with forecasting based on time-variant fuzzy time series and the firefly algorithm, as a highly efficient and recent evolutionary metaheuristic inspired by a firefly and its bioluminescence behaviours. The proposed algorithm determines the length of each interval in the universe of discourse and degree of membership values simultaneously. We calibrate the proposed algorithm on benchmark data in order to compare the results achieved in terms of forecasting accuracy with those of particle swarm optimisation in the literature; then, we apply it to forecast quarterly exchange rates. Numerical results indicate that the proposed algorithm competes well with the particle swarm optimisation approach.