Study of simultaneous occurrence of probabilistic and non-probabilistic uncertainties in time series forecasting
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Date
2019-01
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
Statistical techniques based conventional time series forecasting models are capable to deal probabilistic uncertainty that is caused by randomness. Fuzzy time series forecasting models can handle the non-probabilistic uncertainty that arises due to vagueness and linguistic representation of time series data. Both probabilistic and non-probabilistic uncertainties arise in time series forecasting but neither probability theory nor fuzzy set theory handles these both types of uncertainty simultaneously. Probabilistic fuzzy set includes prominent characteristics of both fuzzy and probability theory and hence is used to model both uncertainties simultaneously in a single framework. In this research work, probabilistic fuzzy set, probabilistic intuitionistic fuzzy set, hesitant probabilistic fuzzy sets and intuitionistic fuzzy random variables are used to develop six time series forecasting methods to include both kinds of uncertainties and non-determinism. These methods are presented in forms of models. Model-1, Model-2 and Model-3 are based on probabilistic fuzzy set that use probabilistic fuzzy logical relations of different orders and different schemes to partition time series data. Model-4 is was probabilistic intuitionistic fuzzy set based time series forecasting model that includes both types of uncertainties and non-determinism. Model-5 is based on hesitant probabilistic fuzzy set that also includes both types of uncertainties and non-determinism. Model-5 also includes a particular type of non-determinism that arises due to multiple fuzzification of time series data. Model-6 uses intuitionistic fuzzy random variable and handles both types of uncertainties. While Models [1-5] handles non-probabilistic uncertainties associated with membership grades or non-memberships grades, this model includes probabilistic uncertainty due to randomness of time series data. Models [1-6] are implemented to forecast time series data of University of Alabama enrolments, SBI share prices and TAIEX to show their outperformance over others forecasting methods. Performance of the models has been analyzed in terms of RMSE, AFER. Validity, robustness of the models against variations in time series data is also tested using evaluation parameter, performance parameter, tracking signal and statistical test (t-test and Wilcoxon signed rank test) in time series data.
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