Sufficient conditions for stable recovery of sparse autoregressive models

Abstract

We consider the problem of estimating the parameters of autoregressive linear models with subGaussian innovations from limited observations, where the history of the process composes the covariate. We analyze the performance of lasso type and greedy estimators and characterize the sampling tradeoffs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear models with i.i.d. covariates to autoregressive processes with highly interdependent covariates. We further provide simulation studies as well as application to financial data which confirm our theoretical predictions.