A Semiparametric Model for Time Series Based on Fuzzy Data

This paper proposes a semiparametric autoregressive integrated moving average model for those real-world applications whose observed data are reported by fuzzy numbers. To this end, a hybrid method including nonparametric kernel-based method, least absolute deviations, and cross-validation method is suggested, which allows estimating parameters of the model including the autoregressive order p, optimal value of the smoothing parameter h, and fuzzy smooth function of the innovations, simultaneously. A correlation concept is also developed for fuzzy time series data and its main properties are investigated. Some common goodness-of-fit criteria are employed to examine the performance of the proposed fuzzy semiparametric time series model. A potential application of the proposed method is represented through simulated fuzzy time series data. To illustrate utility of this approach, it is applied to a set of real-life house price data in fuzzy environment. The results indicate that the proposed method is potentially effective for predicting fuzzy time series data in real applications.