Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting
This paper explores the capabilities of machine learning for the probabilistic forecasting of fractional Brownian motion (fBm). The focus is on predicting the probability of the value of an fBm time series exceeding a certain threshold after a specific number of time steps, given only the knowledge...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/7/517 |
| _version_ | 1797589233978834944 |
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| author | Lyudmyla Kirichenko Roman Lavrynenko |
| author_facet | Lyudmyla Kirichenko Roman Lavrynenko |
| author_sort | Lyudmyla Kirichenko |
| collection | DOAJ |
| description | This paper explores the capabilities of machine learning for the probabilistic forecasting of fractional Brownian motion (fBm). The focus is on predicting the probability of the value of an fBm time series exceeding a certain threshold after a specific number of time steps, given only the knowledge of its Hurst exponent. The study aims to determine if the self-similarity property is preserved in a forecasting time series and which machine learning algorithms are the most effective. Two types of forecasting methods are investigated: methods with a predefined distribution shape and those without. The results show that the self-similar properties of the fBm time series can be reliably reproduced in the continuations of the time series predicted by machine learning methods. The study also provides an experimental comparison of various probabilistic forecasting methods and their potential applications in the analysis and modeling of fractal time series. |
| first_indexed | 2024-03-11T01:03:38Z |
| format | Article |
| id | doaj.art-57fe8511b1c04c4ba03c9171c3b01d3e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T01:03:38Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-57fe8511b1c04c4ba03c9171c3b01d3e2023-11-18T19:25:50ZengMDPI AGFractal and Fractional2504-31102023-06-017751710.3390/fractalfract7070517Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series ForecastingLyudmyla Kirichenko0Roman Lavrynenko1Applied Mathematics Department, Kharkiv National University of Radio Electronics, 61166 Kharkiv, UkraineArtificial Intelligence Department, Kharkiv National University of Radio Electronics, 61166 Kharkiv, UkraineThis paper explores the capabilities of machine learning for the probabilistic forecasting of fractional Brownian motion (fBm). The focus is on predicting the probability of the value of an fBm time series exceeding a certain threshold after a specific number of time steps, given only the knowledge of its Hurst exponent. The study aims to determine if the self-similarity property is preserved in a forecasting time series and which machine learning algorithms are the most effective. Two types of forecasting methods are investigated: methods with a predefined distribution shape and those without. The results show that the self-similar properties of the fBm time series can be reliably reproduced in the continuations of the time series predicted by machine learning methods. The study also provides an experimental comparison of various probabilistic forecasting methods and their potential applications in the analysis and modeling of fractal time series.https://www.mdpi.com/2504-3110/7/7/517fractional Brownian motionhurst exponenttime seriesprobabilistic forecastquantile regressiondistributional modelling |
| spellingShingle | Lyudmyla Kirichenko Roman Lavrynenko Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting Fractal and Fractional fractional Brownian motion hurst exponent time series probabilistic forecast quantile regression distributional modelling |
| title | Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting |
| title_full | Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting |
| title_fullStr | Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting |
| title_full_unstemmed | Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting |
| title_short | Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting |
| title_sort | probabilistic machine learning methods for fractional brownian motion time series forecasting |
| topic | fractional Brownian motion hurst exponent time series probabilistic forecast quantile regression distributional modelling |
| url | https://www.mdpi.com/2504-3110/7/7/517 |
| work_keys_str_mv | AT lyudmylakirichenko probabilisticmachinelearningmethodsforfractionalbrownianmotiontimeseriesforecasting AT romanlavrynenko probabilisticmachinelearningmethodsforfractionalbrownianmotiontimeseriesforecasting |