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

Forecasting is a task with many concerns, such as the size, quality, and behavior of the data, the computing power to do it, etc. This letter proposes the dynamic mode decomposition (DMD) as a tool to predict the annual air temperature and the sales of a stores’ chain. The DMD 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 future 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. The proposed method was tested in a case study consisting of the long term prediction of the weekly sales of a chain of stores. The performance assessment was based on the best fit percentage index. The proposed method is compared with three neural network-based predictors.