Joint Regression and Linear Combination of Time Series for Optimal Prediction
Dries Geebelen, Kim Batselier, Philippe Dreesen, Marco Signoretto, Johan A. K. Suykens, Bart De Moor, Joos P. L. Vandewalle · 2012
Abstract. In most machine learning applications the time series to predict is fixed and one has to learn a prediction model that causes the smallest error. In this paper choosing the time series to predict is part of the optimization problem. This time series has to be a linear combination of a priori given time series. The optimization problem that we have to solve can be formulated as choosing the linear combination of a priori known matrices such that the smallest singular vector is minimized. This problem has many local minima and can be formulated as a polynomial system which we will solve using a polynomial system solver. The proposed prediction algorithm has applications in algorithmic trading in which a linear combination of stocks will be bought. 1