Change Periods Detection for Multivariate Time Series with Fuzzy Methods

Researchers have proposed a lot of detecting and testing methods about change points. While in the real case, it shows that the structure change of a time series was changed gradually, that is the change points has illustrated senses of fuzziness. This concept is important in fitting different models to different regimes of the data regarding economic interpretation of the data during that regime. In this paper we present an integrated identification procedure for change periods detection. The membership function of each system, which include multivariate time series data, corresponding to the cluster centers as performance index grouping is calculated. A fuzzy time series C_t* is defined on averages of cumulative fuzzy entropies of the three time series. Finally, an empirical study about change periods identification for Germany, France and Greece major macroeconomic indicators are demonstrated.