Multi-rule combination prediction of compositional data time series based on multivariate fuzzy time series model and its application

Abstract

Compositional data (CoDa) is a type of relative data reflecting the proportion of different units in an integrated system, which can reveal the internal structure of observed objects and has been widely used to analyze practical economic and management problems. However, the summation constraint limits the prediction of compositional data time series. Especially, with small samples and poor information characteristics of the data set, the difficulties are further exacerbated. Compared with real-valued time series analysis, fuzzy time series (FTS) mainly transforms initial observed data to be different status so that the historical evolution rules can be derived. As a result, forms of initial observed data can be concealed. Correspondingly, this paper aims to establish a multi-rule combination prediction of compositional data based on a multivariate fuzzy time series model, named GA-CoDa-MFTS. Firstly, with the interaction of components, the adjustment rules between components are explored by using the fuzzy logical relationship (FLR). Secondly, the Genetic algorithm (GA) is used to find the optimal weight of the predicted values under different rules and derive the combined predicted values. Finally, the prediction effectiveness of the model is verified by CRMSE and CMAPE through a numerical study.