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.