Multivariate Picture Fuzzy Time Series: New Definitions and a New Forecasting Method Based on Pi-Sigma Artificial Neural Network

Abstract

Picture fuzzy time series has been defined recently and a high order single variable forecasting method was proposed in the literature. Picture fuzzy time series definition is based on picture fuzzy sets which are the extended version of the fuzzy sets. So, more information is added for the modelling procedure with the use of picture fuzzy sets instead of classical fuzzy sets. In this study, high order multivariate picture fuzzy time series forecasting model is firstly defined and a forecasting algorithm based on this model is introduced. The proposed method uses picture fuzzy clustering and Pi-Sigma artificial neural networks as creating picture fuzzy time series and estimating of picture fuzzy forecasting model, respectively. The Pi-Sigma artificial neural network is trained by particle swarm optimization. The proposed method is applied to the TAIEX stock exchange data sets using Dow Jones and NASDAQ stock exchange data sets and Turkish lira exchange rates data sets using the dollar, euro and pound data sets as factor variables. The proposed method produces the best results among established benchmarks.