Résumé
Predicting future time series values seems necessary in many areas, however. There are thus applications for controlling various industrial processes, for modeling ecosystems, physical or geological phenomena, as well as in the fields of finance, actuarial science and insurance. In the context of this thesis, we are more specifically interested in the application of the time series method for forecasting sales within the framework of an E-commerce platform.There are two characteristics that generally distinguish stationary time series prediction problems from other learning problems, and which partly explain the difficulties inherent in these tasks.First, from a theoretical point of view, the data of the same time series present mutual dependencies. This invalidates most classical learning approaches, which rely on supposedly independent distributions. This thesis presents different frameworks to model and take into account the dependence between data. We will therefore prove several oracle inequalities in two different dependent frameworks. First, we will study the use of the hold-out model selection method in the framework of dependent time series, and we will show that this method extends well to the dependent framework under slightly restrictive conditions. Second, we will be interested in the modeling of non-causal phenomena by processes analogous to Markov chains, and we will show oracle inequalities in this framework.On the other hand, from a practical point of view, for a given time series there is generally a small number of data relative to other fields of application. This is particularly the case in the context of sales prediction, where the number of dates observed is generally much lower than the number of products considered. We will therefore propose several models capable of « sharing » information between different products and of taking into account the interactions between them. In particular, we will be interested in the modeling of competition phenomena between different time series. These models will be applied to real data generated by CDiscount.
Source: http://www.theses.fr/2021CYUN1051
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