Abstract
The paper discusses a new predictive model of a fuzzy volatile time series, in the framework of which a new approach to the fuzzification of historical data is proposed as the results of observations based on “soft measurements” of the states of a dynamic system over a certain period of time. As an example, the Dow Jones index was chosen, the readings of which are set based on the results of daily trading on the US stock exchange by the usual arithmetic averaging of contextual indicators. This allows to consider the daily readings of the Dow Jones index as weakly structured, and to interpret the dynamics of its change as a fuzzy time series. The fuzzification procedure is implemented by the fuzzy inference system that provides the values of the membership functions of the corresponding fuzzy subsets of the discrete universe covering the set of index indicators for the period from June 15, 2018 to October 10, 2019. The proposed predictive model is based on the identified internal relationships, designed as first-order fuzzy relations between evaluation criteria or fuzzy sets that describe weakly structured Dow Jones indexes. At the end of the study, the proposed model is evaluated for adequacy using the statistical criteria MAPE, MPE and MSE.
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Notes
- 1.
The remaining 136 groups are empty, i.e. do not include PE of any fuzzy sets.
- 2.
If there were a large negative MPE, then the constructed model would be considered “overestimating”. If the MPE indicator would reflect a large positive percentage value, i.e. beyond the 5% threshold on the right, then the model would be considered “underestimating”.
- 3.
It is clear that by a simple mapping x = a + t(b–a), where xε[a, b] (in our case, xε[21752.2, 27359.2]), tε[0, 1] , it is impossible to reflect point estimates of fuzzy outputs, because obviously, the relationship between them is non-linear.
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Rzayev, R., Alizada, P., Mehdiyev, T. (2024). Fuzzy Time Series Forecasting on the Example of the Dow Jones Index Dynamics. In: Arai, K. (eds) Intelligent Systems and Applications. IntelliSys 2023. Lecture Notes in Networks and Systems, vol 822. Springer, Cham. https://doi.org/10.1007/978-3-031-47721-8_7
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