1 research outputs found
Sampling Requirements for Stable Autoregressive Estimation
We consider the problem of estimating the parameters of a linear univariate
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 -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. In particular, we
show that for a fixed sparsity level, stable recovery of AR parameters is
possible when the number of samples scale sub-linearly with the AR order. Our
results improve over existing sampling complexity requirements in AR estimation
using the LASSO, when the sparsity level scales faster than the square root of
the model order. We further derive sufficient conditions on the sparsity level
that guarantee the minimax optimality of the -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