@article {47957,
	title = {Sampling Requirements for Stable Autoregressive Estimation},
	journal = {CoRR},
	volume = {abs/1605.01436},
	year = {2016},
	abstract = {<p>We consider the problem of estimating the parameters of a linear autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the\&nbsp;l1-regularized least squares as well as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear models where the covariates are i.i.d. and independent of the observation history to autoregressive processes with highly inter-dependent covariates. We also derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the\&nbsp;l1-regularized least squares estimate. Applying these techniques to simulated data as well as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretical performance gains in terms of estimation accuracy and model selection.</p>
},
	url = {http://arxiv.org/abs/1605.01436},
	author = {Abbas Kazemipour and Sina Miran and Piya Pal and Behtash Babadi and Min Wu}
}
