FQTSFM: A fuzzy-quantum time series forecasting model

Abstract

The study shows that there are two main problems that affect the performance of fuzzy time series (FTS) models, namely the selection of the universe of discourse and the determination of the fuzzy degree of the memberships. However, the selection of the appropriate universe of discourse along with the degree of memberships is simultaneously associated with the multiobjective optimization problem (MOOP). Therefore, in this study, an improved version of the quantum optimization algorithm (QOA) has been proposed to find their optimal solutions. This improved QOA is called fast forward quantum optimization algorithm (FFQOA). Finally, by integrating FFQOA with the FTS modelling approach, a hybrid model called fuzzy-quantum time series forecasting model (FQTSFM) is designed. The main objective of FFQOA in FQTSFM is to select the Pareto-optimal front (POF) from all optimal non-dominated Pareto solutions by using the archive and grid concept during simulation. The main advantages of the proposed FQTSFM are that it converges very fast compared to the existing hybridized based FTS models and is able to evolve one-step ahead forecasted results. The FQTSFM is tested with three different datasets, namely daily average temperatures of Taipei, Taiwan Futures Exchange (TAIFEX) index and Taiwan Stock Exchange Corporation (TSEC) weighted index. The performance of the FQTSFM is compared with various established well-known FTS and non-FTS models in terms of different statistical metrics. In the case of daily average temperatures, TAIFEX index and TSEC weighted index datasets, the FQTSFM achieves correlation coefficients of 0.9988, 0.9978 and 0.9768, respectively. For daily average temperatures, TAIFEX index and TSEC weighted index datasets, the Theil’s U statistic values of the FQTSFM are 0.0022, 0.0022 and 0.0054, respectively. The FQTSFM has mean squared errors of 0.3959, 22.3965 and 83.6793 for the daily average temperatures, the TAIFEX index and the TSEC-weighted index datasets, respectively. In the case of daily average temperatures, TAIFEX index and TSEC weighted index datasets, the FQTSFM shows cross entropy values of 3.3498, 189.5018 and 708.0296, respectively. These metrics, including other empirical analyses, confirm that the forecasted accuracy of the proposed FQTSFM exceeds that of well-known time series models.