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State-Space Models for Time Series Forecasting. Application to the Electricity Markets

Abstract : Electricity storage capacities are still negligible compared to the demand. Therefore, it is fundamental to maintain the equilibrium between consumption and production, and to that end, we need load forecasting. Numerous patterns motivate the study of time-varying models, including: changes in people's habits, increasing renewable capacities, more recently the coronavirus crisis. This thesis aims to propose adaptive methods for time series forecasting. We focus on state-space models, where the environment (or context) is represented by a hidden state on which the demand depends. Thus, we try to estimate that state based on the observations at our disposal. Based on our estimate, we forecast the load. The first objective of the thesis is to enrich the link between optimization and state-space estimation. Indeed, we see our methods as second-order stochastic gradient descent algorithms, and we treat a particular case to detail that link. The second contribution concerns variance estimation in state-space models. Indeed, the variances are the parameters on which the models' dynamics crucially relies. The third part of the manuscript is the application of these methods to electricity load forecasting. Our methods build on existing forecasting methods like generalized additive models. The procedure allows to leverage advantages of both. On the one hand, statistical models learn complex relations to explanatory variables like temperature. On the other hand, state-space methods yield model adaptation.
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Submitted on : Thursday, September 22, 2022 - 11:16:14 AM
Last modification on : Monday, October 24, 2022 - 1:36:13 PM


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  • HAL Id : tel-03783480, version 2


Joseph De Vilmarest. State-Space Models for Time Series Forecasting. Application to the Electricity Markets. Statistics [math.ST]. Sorbonne Université, 2022. English. ⟨NNT : 2022SORUS108⟩. ⟨tel-03783480v2⟩



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