Modelisation of competition between times series

Competition between times series arises naturally in sales forecasting or in population modelisation. In this article, a model for the behavior of such high-dimensional time series is proposed. This model is based on the prerequisite that the total sum of the time series is distributed between its component following a 'competitiveness' factor inherent to each component. A confidence bound is proposed for the estimation of this model. Then, this model is applied to real-world E-commerce data using a recurrent neural network architecture to compute the model. It improves the results of standard RNN models in most cases.