RobustTSVar: A Robust Time Series Variance Estimation Algorithm

Variance estimation has been one of the key challenges in time series analysis for a long time. Although many ARCHtype algorithms are widely applied in variance estimation, they suffer from sensitivity to outliers and fail to handle complex data such as abrupt trend change and variance periodicity. The time warping of the periodicity makes it further complicated. To deal with these challenges, we propose a robust algorithm called RobustTSVar, based on quantile regression for robust variance estimation. To deal with variance periodicity with time warping, we propose non-local periodic filtering to further refine the variance estimate. An efficient implementation based on ADMM is also proposed to handle large-scale data. We compare our proposed RobustTSVar method with other state-of-the-art methods on both synthetic and real-world datasets, and the numerical results demonstrate the superior performance of our algorithm.