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Fourier methods for efficient sufficient dimension reduction in time series
Journal article   Peer reviewed

Fourier methods for efficient sufficient dimension reduction in time series

S. Yaser Samadi and Tharindu De Alwis
The Canadian journal of statistics = La revue canadienne de statistique, e70027
10/30/2025
DOI: https://doi.org/10.1002/cjs.70027
Web of Science ID: WOS:001604131600001

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Abstract

Dimension reduction has always been one of the most significant and challenging problems in the analysis of high-dimensional data. In the context of time series analysis, our focus is on the estimation and inference of conditional mean and variance functions. By using central mean and variance dimension reduction subspaces that preserve sufficient information about the response, one can estimate the unknown mean and variance functions. While several approaches exist to estimate the time series central mean and variance subspaces (TS-CMS and TS-CVS), they are often computationally intensive and impractical. By employing the Fourier transform, we derive explicit estimators for TS-CMS and TS-CVS. These estimators are consistent, asymptotically normal, and efficient. Simulation studies evaluate the method&#39;s performance, showing it is significantly more accurate and computationally efficient than existing ones. Furthermore, the method is applied to the Canadian lynx dataset.</span></p>

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