Sliced average variance estimation for multivariate time series

ABSTRACT

Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response y and the predictors $\mathbf{\text{x}}$. Recently a time series version of sliced inverse regression, TSIR, was suggested, which applies approximate joint diagonalization of several supervised lagged covariance matrices to consider the temporal nature of the data. In this paper, we develop this concept further and propose a time series version of sliced average variance estimation, TSAVE. As both TSIR and TSAVE have their own advantages and disadvantages, we consider furthermore a hybrid version of TSIR and TSAVE. Based on examples and simulations we demonstrate and evaluate the differences between the three methods and show also that they are superior to apply their iid counterparts to when also using lagged values of the explaining variables as predictors.

KEYWORDS:

• Blind source separation
• supervised dimension reduction
• prediction

AMS SUBJECT CLASSIFICATION:

• 62M10

Acknowledgements

We wish to thank the Associate Editor and the reviewers for careful reading of the paper and their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. Matilainen http://orcid.org/0000-0002-5597-2670

Additional information

Funding

The work of M. Matilainen and H. Oja was supported by the Academy of Finland (Suomen Akatemia) under Grant 268703; and the work of K. Nordhausen was supported by the CRoNoS COST Action IC1408.