Estimation of stable parameters for multiple autoregressive processes via convex programming

Somnath Chakraborty (), Johannes Lederer () and Rainer von Sachs ()
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Somnath Chakraborty: Ruhr-Universität Bochum
Johannes Lederer: Universität Hamburg
Rainer von Sachs: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2023037, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We develop a finite-sample theory for estimating the coefficients and for the prediction of multiple stable autoregressive processes that (i) share an unknown lag order but (ii) can differ in their individual sample sizes. Our technique is based on penalisation similar to hierarchical, overlapping group-Lasso but requires a new mathematical set-up to accommodate (i) and (ii). The set-up differs from existing work considerably, for example, in that we estimate the common lag order directly from the data rather than using extrinsic criteria. We prove that the estimated autoregressive processes enjoy stability, and we establish rates for both the estimation and prediction error that can outmatch the known rates in our setting. Our insights on the lag selection and the stability are also of interest for the case of individual autoregressive processes.

Keywords: Autoregressive process; effective noise; statistical guarantees; tuning parameter; dual norm; hierarchical-group norm; group LASSO; lag selection; false discoveries; regularised least square; sample complexity; stable AR process; gaussian innovation; restricted eigenvalue property (search for similar items in EconPapers)
Pages: 37
Date: 2023-12-01
New Economics Papers: this item is included in nep-ecm and nep-inv
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