Time-Series Dimensionality Reduction via Granger Causality

We deal with the problem of time-series prediction in a dyadic setup where the goal is to predict future values of the output sequence from the observed input sequence. Often the input time-series data is high-dimensional with potential noisy measurements included, which can make the prediction task difficult. In this paper, we propose a novel dimensionality reduction algorithm that can sparsely extract most salient and discriminative input features for output prediction. Our approach is based on the Granger causality, a famous statistical technique particularly in economics, where we aim to discover a low-dimensional subspace that preserves the causality between input and output. We demonstrate empirically the benefits of the proposed approaches on several datasets.