Abstract

We propose a multiscale approach to time series autoregression, in which

linear regressors for the process in question include features of its own path that live on

multiple timescales. We take these multiscale features to be the recent averages of the

process over multiple timescales, whose number or spans are not known to the analyst

and are estimated from the data via a change-point detection technique. The resulting

construction, termed Adaptive Multiscale AutoRegression (AMAR) enables adaptive

regularisation of linear autoregressions of large orders. The AMAR model is designed to

offer simplicity and interpretability on the one hand, and modelling flexibility on the other.

Our theory permits the longest timescale to increase with the sample size. A simulation

study is presented to show the usefulness of our approach. Some possible extensions

are also discussed, including the Adaptive Multiscale Vector AutoRegressive model

(AMVAR) for multivariate time series, which demonstrates promising performance in the

data example on UK and US unemployment rates. The R package amar (Baranowski

et al., 2022) provides an efficient implementation of the AMAR framework.

Information

Preprint No.SS-2023-0017
Manuscript IDSS-2023-0017
Complete AuthorsRafal Baranowski, Yining Chen, Piotr Fryzlewicz
Corresponding AuthorsYining Chen
EmailsY.Chen101@lse.ac.uk

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Acknowledgments

We are extremely grateful to the associate editor and three anonymous reviewers

for their valuable comments and suggestions, which have helped improve the

manuscript.

Supplementary Materials

The online Supplementary Material contains discussions and illustrations on some

special cases of AMAR, further simulations, an additional real data example, and

the proofs of the theoretical results.

Supplementary materials are available for download.