Fuzzy Transform in Time Series Decomposition

In this paper, we provide a method for applying the fuzzy transform of higher degree to time series decomposition. We assume that a time series can be decomposed into a trend-cycle, a seasonal component and an irregular fluctuation, we devote theoretical justifications for decomposing it into an additive model. Several examples are consider to demonstrate our methodology.

[1]  Vilém Novák.  Linguistic characterization of time series , 2016, Fuzzy Sets Syst..

[2]  E. J. Godolphin,et al.  Decomposition of time series models in state-space form , 2006, Comput. Stat. Data Anal..

[3]  P. Maass,et al.  A Review of Some Modern Approaches to the Problem of Trend Extraction , 2012 .

[4]  Vilém Novák,et al.  Multivariate fuzzy transform of complex-valued functions determined by monomial basis , 2017, Soft Comput..

[5]  Vilém Novák,et al.  Forecasting seasonal time series based on fuzzy techniques , 2019, Fuzzy Sets Syst..

[6]  James D. Hamilton.  Time Series Analysis , 1994 .

[7]  Vladik Kreinovich,et al.  Filtering out high frequencies in time series using F-transform , 2014, Inf. Sci..

[8]  Michal Holcapek,et al.  Polynomial alias higher degree fuzzy transform of complex-valued functions , 2017, Fuzzy Sets Syst..

[9]  Michal Holcapek,et al.  Higher Degree Fuzzy Transform: Application to Stationary Processes and Noise Reduction , 2017, EUSFLAT/IWIFSGN.

[10]  Martina Danková,et al.  Towards a higher degree F-transform , 2011, Fuzzy Sets Syst..

[11]  Irina Perfilieva,et al.  Fuzzy transforms: Theory and applications , 2006, Fuzzy Sets Syst..

[12]  Michal Holcapek,et al.  Suppression of High Frequencies in Time Series Using Fuzzy Transform of Higher Degree , 2016, IPMU.

[13]  Michal Holčapek,et al.  TREND-CYCLE ESTIMATION USING FUZZY TRANSFORM OF HIGHER DEGREE , 2018 .

[14]  T. Cipra.  Statistical Analysis of Time Series , 2010 .

[15]  Vilém Novák,et al.  Analysis of seasonal time series using fuzzy approach , 2010, Int. J. Gen. Syst..

[16]  Vilém Novák,et al.  Mining information from time series in the form of sentences of natural language , 2016, Int. J. Approx. Reason..

[17]  Vilém Novák,et al.  TIME SERIES GROUPING AND TREND FORECAST USING F1-TRANSFORM AND FUZZY NATURAL LOGIC , 2014 .

[18]  Marina Theodosiou,et al.  Forecasting monthly and quarterly time series using STL decomposition , 2011 .