自适应检测时间尺度上的多尺度自回归

我们提出了一种多尺度方法，用于时间序列自回归，其中线性回归器包括来自自身路径上多个时间尺度上的特征。我们将这些多尺度特征视为在多个时间尺度上的进程最近平均值，其数量或跨度由分析师未知，通过变点检测技术从数据中估计。 resulting construction, termed Adaptive Multiscale AutoRegression (AMAR), enables adaptive regularization 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.