A Dynamic Mode Decomposition Approach with Hankel Blocks to Forecast Multi-Channel Temporal Series

Abstract

Forecasting is always a task with many concerns, such as the size, quality, and behavior of the data, the computing power to do it, etc. This paper proposes the Dynamic Mode Decomposition as a tool to predict the annual air temperature and the sales of a supermarket chain. The Dynamic Mode Decomposition decomposes the data into its principal modes, which are estimated from a training data set. It is assumed that the data is generated by a linear time-invariant high order autonomous system. These modes are useful to find the way the system behaves and to predict its futures states, without using all the available data, even in a noisy environment. The Hankel block allows the estimation of hidden oscillatory modes, by increasing the order of the underlying dynamical system. Theproposed method was tested in a case study consisting of the long term prediction of the weekly sales of a chain of stores. The performance was assessment was based on residual analysis and on Best Fit Percentage Index. The proposed method is compared with three Neural Network Based predictors.