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.

翻译：我们提出了一种时间序列自回归的多尺度方法，其中针对目标过程的线性回归器包含其自身路径在多时间尺度上的特征。我们将这些多尺度特征定义为该过程在多个时间尺度上的近期平均值，其数量或跨度对分析者未知，并通过变点检测技术从数据中估计得出。由此构建的模型称为自适应多尺度自回归（AMAR），能够实现大阶数线性自回归的自适应正则化。AMAR模型一方面旨在提供简洁性和可解释性，另一方面也兼顾建模灵活性。我们的理论允许最长的时间尺度随样本量增加而增长。通过模拟研究展示了该方法的实用性。文中还讨论了一些可能的扩展，包括针对多元时间序列的自适应多尺度向量自回归模型（AMVAR），该模型在英国和美国失业率的数据示例中表现出良好性能。R软件包amar提供了AMAR框架的高效实现。