Title: Multiscale autoregression on adaptively detected timescales
Authors: Piotr Fryzlewicz - London School of Economics (United Kingdom) [presenting]
Rafal Baranowski - London School of Economics (United Kingdom)
Abstract: A multiscale approach to time series autoregression is proposed, 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 of 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 permits the longest timescale to increase with the sample size, and is designed to offer simplicity and interpretability on the one hand, and modelling flexibility on the other. As a side result, we also provide an explicit bound on the tail probability of the L2 norm of the difference between the autoregressive coefficients and their OLS estimates in the AR(p) model with i.i.d. Gaussian noise when the order p potentially diverges with, and the autoregressive coefficients potentially depend on, the sample size. The R package amar provides an efficient implementation of the AMAR modelling, estimation and forecasting framework.