Time Series Forecasting Using Independent Component Analysis

The paper presents a method for multivariate time series forecasting using Independent Component Analysis (ICA), as a preprocessing tool. The idea of this approach is to do the forecasting in the space of independent components (sources), and then to transform back the results to the original time series space. The forecasting can be done separately and with a different method for each component, depending on its time structure. The paper gives also a review of the main algorithms for independent component analysis in the case of instantaneous mixture models, using second and high-order statistics. The method has been applied in simulation to an artificial multivariate time series with five components, generated from three sources and a mixing matrix, randomly generated.




References:
[1] A. Hyv¨arinen, J. Karhunen and E. Oja, Independent Component Analysis,
John Wiley & Sons, Inc, 2001.
[2] P. Comon, "Independent Component analysis - a new concept ?", Signal Processing, vol. 36, pp. 287-314, 1994.
[3] A. Belouchrani, K. Abed Meraim, J.F. Cardoso and E. Moulines, "A blind source separation technique based on second order statistics", IEEE Trans. on Signal Processing, vol. 45, no. 2, pp. 434-444, 1997.
[4] M. Wax and T. Kailath, "Determining the number of signals by information
theoretic criteria", Workshop on spectral estimation II, Florida, pp. 192-196, 1983.
[5] Y. Yin and P. Krishnaiah, "Methods for detection of the number of signals", IEEE Trans. on ASSP, vol. 35, no. 11, pp. 1533-1538, 1987.
[6] G. H. Golub and C.F.V. Loan, Matrix Computation, The John Hopkins
University Press, 1989.
[7] A. Souloumiac and J.F. Cardoso, "Comparaison de methodes de separation
de sources", Proc. GRETSI, Juan les Pines, 1991.
[8] A. Souloumiac and J.F. Cardoso, "Givens angles for simultaneous diagonalization", SIAM J. Matrix Anal. Appl., 1994.
[9] J. F. Cardoso and A. Souloumiac, "Blind beamforming for non Gaussian signals, IEE Proceedings - F, vol. 140, no. 6, pp. 362-370, 1993.
[10] J. F. Cardoso and P. Comon, "Tensor based independent component
analysis", Proc. EU-SIPCO, 1990.