Sparse Auto-Regressive: Robust Estimation of AR Parameters

TL;DR

This paper introduces a robust auto-regressive estimation method that handles outliers and missing data in time series by promoting residual sparsity, demonstrated through spectrum estimation and speech coding simulations.

Contribution

It proposes a novel auto-regressive estimation approach that is robust to outliers and missing data, incorporating residual sparsity for improved coding performance.

Findings

Effective spectrum estimation demonstrated

Improved speech coding results

Robustness to outliers and missing data

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.