Abstract
In this article, we propose a framework for seasonal time series probabilistic forecasting. It aims at forecasting (in a probabilistic way) the whole next season of a time series, rather than only the next value. Probabilistic forecasting consists in forecasting a probability distribution function for each future position. The proposed framework is implemented combining several machine learning techniques (1) to identify typical seasons and (2) to forecast a probability distribution of the next season. This framework is evaluated using a wide range of real seasonal time series. On the one side, we intensively study the alternative combinations of the algorithms composing our framework (clustering, classification), and on the other side, we evaluate the framework forecasting accuracy. As demonstrated by our experiences, the proposed framework outperforms competing approaches by achieving lower forecasting errors.
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Notes
- 1.
The Cartesian product of the three partitions is used as a constant piecewise estimator—i.e. a 3D histogram.
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Leverger, C. et al. (2023). Probabilistic Forecasting of Seasonal Time Series. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis and Forecasting. ITISE 2021. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-14197-3_4
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