Probabilistic Forecasting With Fuzzy Time Series

In recent years, the demand for developing low computational cost methods to deal with uncertainties in forecasting has been increased. Probabilistic forecasting is a class of forecasting in which the method provides intervals or probability distributions as outcomes of its forecasting. The aim of this paper is, therefore, proposing a new forecasting approach based on fuzzy time series (FTS) that takes advantage of fuzzy and stochastic patterns on data and is capable to deal with point, interval, and distribution forecasts. The method proposed was empirically tested with typical financial time series, and the results were compared with other standard FTS and statistical methods. The results show that the proposed method obtained accurate results and outperformed standard FTS methods. The proposed method also combines versatility, scalability, and low computational cost, making it useful on a wide range of application scenarios.

[1]  Qiang Song,et al.  Fuzzy stochastic fuzzy time series and its models , 1997, Fuzzy Sets Syst..

[2]  Binbin Wang,et al.  Simulation of Nonstationary Spring Discharge Using Time Series Models , 2017, Water Resources Management.

[3]  Zbigniew Telec,et al.  Nonparametric statistical analysis for multiple comparison of machine learning regression algorithms , 2012, Int. J. Appl. Math. Comput. Sci..

[4]  Frederico G. Guimarães,et al.  An extension of nonstationary fuzzy sets to heteroskedastic fuzzy time series , 2018, ESANN.

[5]  Tahseen Ahmed Jilani,et al.  A New Quantile Based Fuzzy Time Series Forecasting Model , 2008 .

[6]  Hossein Javedani Sadaei,et al.  A hybrid model based on differential fuzzy logic relationships and imperialist competitive algorithm for stock market forecasting , 2016, Appl. Soft Comput..

[7]  Kunhuang Huarng,et al.  Effective lengths of intervals to improve forecasting in fuzzy time series , 2001, Fuzzy Sets Syst..

[8]  Leonard J. Tashman,et al.  Out-of-sample tests of forecasting accuracy: an analysis and review , 2000 .

[9]  Vasile Georgescu Joint propagation of ontological and epistemic uncertainty across risk assessment and fuzzy time series models , 2014, Comput. Sci. Inf. Syst..

[10]  Narges Shafaei Bajestani,et al.  Forecasting TAIEX using improved type 2 fuzzy time series , 2011, Expert Syst. Appl..

[11]  A. Raftery,et al.  Probabilistic forecasts, calibration and sharpness , 2007 .

[12]  NingNing Huang,et al.  A novel method based on FTS with both GA-FCM and multifactor BPNN for stock forecasting , 2018, Soft Computing.

[13]  Chen-Tung Chen,et al.  A fuzzy approach for supplier evaluation and selection in supply chain management , 2006 .

[14]  Hamid Reza Karimi,et al.  Prediction of stock index futures prices based on fuzzy sets and multivariate fuzzy time series , 2015, Neurocomputing.

[15]  Frederico G. Guimarães,et al.  Probabilistic Forecasting with Seasonal Ensemble Fuzzy Time-Series , 2018 .

[16]  D. Dubois,et al.  Fuzzy sets, probability and measurement , 1989 .

[17]  B. Chissom,et al.  Fuzzy time series and its models , 1993 .

[18]  Muhammad Hisyam Lee,et al.  Multilayer Stock Forecasting Model Using Fuzzy Time Series , 2014, TheScientificWorldJournal.

[19]  Shyi-Ming Chen,et al.  Forecasting enrollments based on fuzzy time series , 1996, Fuzzy Sets Syst..

[20]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[21]  Frederico G. Guimarães,et al.  Interval forecasting with Fuzzy Time Series , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[22]  Frederico G. Guimarães,et al.  Very short-term solar forecasting using fuzzy time series , 2017, 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[23]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[24]  L. Zadeh Probability measures of Fuzzy events , 1968 .

[25]  Pritpal Singh,et al.  A brief review of modeling approaches based on fuzzy time series , 2015, International Journal of Machine Learning and Cybernetics.

[26]  H. Finner On a Monotonicity Problem in Step-Down Multiple Test Procedures , 1993 .

[27]  B. Chissom,et al.  Forecasting enrollments with fuzzy time series—part II , 1993 .

[28]  Manuel Mucientes,et al.  STAC: A web platform for the comparison of algorithms using statistical tests , 2015, 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[29]  Hui-Kuang Yu Weighted fuzzy time series models for TAIEX forecasting , 2005 .

[30]  M. C. Jones,et al.  A reliable data-based bandwidth selection method for kernel density estimation , 1991 .

[31]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[32]  Patricia Melin,et al.  Ant colony optimization with dynamic parameter adaptation based on interval type-2 fuzzy logic systems , 2017, Appl. Soft Comput..

[33]  Vasile Georgescu Fuzzy Time Series Estimation and Prediction: Criticism, Suitable New Methods and Experimental Evidence , 2010 .

[34]  Igor Skrjanc,et al.  New results in modelling derived from Bayesian filtering , 2010, Knowl. Based Syst..

[35]  Susan M. Bridges,et al.  Mining fuzzy association rules and fuzzy frequency episodes for intrusion detection , 2000 .

[36]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[37]  B. Silverman Density estimation for statistics and data analysis , 1986 .

[38]  Lotfi A. Zadeh,et al.  Fuzzy probabilities , 1996, Inf. Process. Manag..

[39]  Chris Chatfield,et al.  Calculating Interval Forecasts , 1993 .

[40]  R. L. Winkler A Decision-Theoretic Approach to Interval Estimation , 1972 .

[41]  Qiang Song,et al.  Seasonal forecasting in fuzzy time series , 1999, Fuzzy Sets Syst..

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

[43]  Tao Hong,et al.  Probabilistic electric load forecasting: A tutorial review , 2016 .

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

[45]  Alexander S. Poznyak,et al.  Projectional Dynamic Neural Network Identifier for Chaotic Systems: Application to Chua's Circuit , 2019 .

[46]  Tao Hong,et al.  GEFCom2014 probabilistic electric load forecasting: An integrated solution with forecast combination and residual simulation , 2016 .

[47]  Abdul Hanan Abdullah,et al.  Short-term load forecasting using a hybrid model with a refined exponentially weighted fuzzy time series and an improved harmony search , 2014 .

[48]  Chris Chatfield,et al.  Prediction Intervals for Time-Series Forecasting , 2001 .

[49]  Stefania Tamea,et al.  Verification tools for probabilistic forecasts of continuous hydrological variables , 2006 .

[50]  Suhartono,et al.  A Weighted Fuzzy Integrated Time Series for Forecasting Tourist Arrivals , 2011 .

[51]  Adrian E. Raftery,et al.  Probabilistic Weather Forecasting in R , 2011 .

[52]  Sheng-Tun Li,et al.  A FCM-based deterministic forecasting model for fuzzy time series , 2008, Comput. Math. Appl..

[53]  Jianxue Wang,et al.  K-nearest neighbors and a kernel density estimator for GEFCom2014 probabilistic wind power forecasting , 2016 .

[54]  Mustafa Mat Deris,et al.  Application of Fuzzy Time Series Approach in Electric Load Forecasting , 2015, New Math. Nat. Comput..

[55]  Gwo-Hshiung Tzeng,et al.  Fuzzy Seasonal Time Series for Forecasting the Production Value of the Mechanical Industry in Taiwan , 1999 .

[56]  Kalyani Mali,et al.  A novel data partitioning and rule selection technique for modeling high-order fuzzy time series , 2018, Appl. Soft Comput..

[57]  Shyi-Ming Chen,et al.  Fuzzy Forecasting Based on Two-Factors Second-Order Fuzzy-Trend Logical Relationship Groups and the Probabilities of Trends of Fuzzy Logical Relationships , 2015, IEEE Transactions on Cybernetics.

[58]  Rosangela Ballini,et al.  Interval fuzzy rule-based modeling approach for financial time series forecasting , 2017, 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[59]  Mustafa Mat Deris,et al.  Improved Weight Fuzzy Time Series as used in the Exchange rates Forecasting of US Dollar to Ringgit Malaysia , 2013, Int. J. Comput. Intell. Appl..

[60]  J. L. Hodges,et al.  Rank Methods for Combination of Independent Experiments in Analysis of Variance , 1962 .

[61]  Rob J Hyndman,et al.  Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond , 2016 .

[62]  Jianxue Wang,et al.  GEFCom2014 probabilistic solar power forecasting based on k-nearest neighbor and kernel density estimator , 2015, 2015 IEEE Power & Energy Society General Meeting.

[63]  Abdul Hanan Abdullah,et al.  Imperialist competitive algorithm combined with refined high-order weighted fuzzy time series (RHWFTS-ICA) for short term load forecasting , 2013 .

[64]  Ping-Teng Chang,et al.  Fuzzy seasonality forecasting , 1997, Fuzzy Sets Syst..

[65]  Frederico G. Guimarães,et al.  Combining ARFIMA models and fuzzy time series for the forecast of long memory time series , 2016, Neurocomputing.

[66]  Henrik Madsen,et al.  Properties of quantile and interval forecasts of wind generation and their evaluation. , 2006 .

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

[68]  Shyi-Ming Chen,et al.  Handling forecasting problems using fuzzy time series , 1998, Fuzzy Sets Syst..

[69]  Tim N. Palmer,et al.  Ensemble forecasting , 2008, J. Comput. Phys..

[70]  Tilmann Gneiting,et al.  Editorial: Probabilistic forecasting , 2008 .

[71]  Shyi-Ming Chen,et al.  TAIEX Forecasting Based on Fuzzy Time Series and Fuzzy Variation Groups , 2011, IEEE Transactions on Fuzzy Systems.

[72]  Frederico G. Guimarães,et al.  Stock market forecasting by using a hybrid model of exponential fuzzy time series , 2016, Int. J. Approx. Reason..

[73]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[74]  Hossein Javedani Sadaei Improved models in fuzzy time series for forecasting , 2013 .

[75]  Martin Stepnicka,et al.  A linguistic approach to time series modeling with the help of F-transform , 2011, Fuzzy Sets Syst..