Efficient and Consistent Robust Time Series Analysis

TL;DR

This paper introduces an efficient algorithm for robust time series analysis under AR models that can accurately estimate parameters even with many corrupted data points, overcoming challenges posed by data correlation.

Contribution

The paper presents a novel hard-thresholding based algorithm for robust AR model estimation that handles correlated data and arbitrary outliers, with proven consistency and efficiency.

Findings

Successfully recovers AR parameters with high corruption levels

Provides the first efficient estimator for robust linear regression with arbitrary noise

Demonstrates effectiveness on synthetic datasets

Abstract

We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent estimate of the optimal AR model despite a large fraction of the time series points being corrupted. Our algorithm alternately estimates the corrupted set of points and the model parameters, and is inspired by recent advances in robust regression and hard-thresholding methods. However, a direct application of existing techniques is hindered by a critical difference in the time-series domain: each point is correlated with all previous points rendering existing tools inapplicable directly. We show how to overcome this hurdle using novel proof techniques. Using our techniques, we are also able to provide the first efficient and provably consistent estimator for the robust regression problem where a standard linear observation model with white additive noise is corrupted arbitrarily. We illustrate our methods on synthetic datasets and show that our methods indeed are able to consistently recover the optimal parameters despite a large fraction of points being corrupted.