  In this paper we introduce a Non-Stationary Fuzzy Time Series (NSFTS) method
with time varying parameters adapted from the distribution of the data. In this
approach, we employ Non-Stationary Fuzzy Sets, in which perturbation functions
are used to adapt the membership function parameters in the knowledge base in
response to statistical changes in the time series. The proposed method is
capable of dynamically adapting its fuzzy sets to reflect the changes in the
stochastic process based on the residual errors, without the need to retraining
the model. This method can handle non-stationary and heteroskedastic data as
well as scenarios with concept-drift. The proposed approach allows the model to
be trained only once and remain useful long after while keeping reasonable
accuracy. The flexibility of the method by means of computational experiments
was tested with eight synthetic non-stationary time series data with several
kinds of concept drifts, four real market indices (Dow Jones, NASDAQ, SP500 and
TAIEX), three real FOREX pairs (EUR-USD, EUR-GBP, GBP-USD), and two real
cryptocoins exchange rates (Bitcoin-USD and Ethereum-USD). As competitor models
the Time Variant fuzzy time series and the Incremental Ensemble were used,
these are two of the major approaches for handling non-stationary data sets.
Non-parametric tests are employed to check the significance of the results. The
proposed method shows resilience to concept drift, by adapting parameters of
the model, while preserving the symbolic structure of the knowledge base.
