Lag selection and estimation of stable parameters for multiple autoregressive processes through convex programming
This work addresses lag selection and parameter estimation for high-dimensional time series, with potential applications in various fields, though it appears incremental by building on recent methods for individual processes.
The paper tackles the problem of simultaneously selecting an unknown shared lag and estimating parameters for multiple stable autoregressive processes, proving stability and establishing forecasting error rates that can outperform known benchmarks.
Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have become available very recently. We, instead, consider multiple stable autoregressive processes that share an unknown lag. We use information across the different processes to simultaneously select the lag and estimate the parameters. We prove that the estimated process is stable, and we establish rates for the forecasting error that can outmatch the known rate in our setting. Our insights on the lag selection and the stability are also of interest for the case of individual autoregressive processes.