Sparse Auto-Regressive: Robust Estimation of AR Parameters

Abstract: In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation difficult, so it should be robust against them. Moreover for coding purposes I will show that it is desired the residual of auto-regression be sparse. To these aims, I first assume a multivariate Gaussian prior on the residual and then obtain the estimation. Two simple simulations have been done on spectrum estimation and speech coding.