Sparse Auto-Regressive: Robust Estimation of AR Parameters
This addresses the problem of robust time series analysis for applications like signal processing, though it appears incremental as it builds on existing auto-regressive frameworks.
The paper tackles robust auto-regressive parameter estimation for time series with outliers or missing samples, proposing a method that assumes a multivariate Gaussian prior on residuals to achieve sparsity, with validation through simulations on spectrum estimation and speech coding.
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.