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.

[1]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[2]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[3]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[4]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[5]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[6]  H. Akaike A new look at the statistical model identification , 1974 .

[7]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[8]  M. Bartlett Periodogram analysis and continuous spectra. , 1950, Biometrika.

[9]  C. Granger Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[10]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[11]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[12]  Daniele Marinazzo,et al.  Grouping time series by pairwise measures of redundancy , 2010, 1006.4794.

[13]  Yingcun Xia,et al.  On extended partially linear single-index models , 1999 .

[14]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[15]  A. Seth,et al.  Multivariate Granger causality and generalized variance. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.