Multiscale Autoregression on Adaptively Detected Timescales

TL;DR

The paper introduces Adaptive Multiscale AutoRegression (AMAR), a flexible and interpretable method for modeling time series with features across multiple unknown timescales, estimated via change-point detection.

Contribution

It presents a novel multiscale autoregression framework that adaptively detects relevant timescales from data, enhancing modeling flexibility and interpretability.

Findings

AMAR effectively captures multiscale features in time series.

Simulation studies demonstrate improved forecasting accuracy.

The approach extends to multivariate series with promising results.

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 autoregression 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 provides an efficient implementation of the AMAR framework.