This paper presents variance extraction procedures for univariate time series. The volatility of a times series is monitored allowing for non-linearities, jumps and outliers in the level. The volatility is measured using the height of triangles formed by consecutive observations of the time series. This idea was proposed by Rousseeuw and Hubert [1996. Regression-free and robust estimation of scale for bivariate data. Comput. Statist. Data Anal. 21, 67–85] in the bivariate setting. This paper extends their procedure to apply for online scale estimation in time series analysis. The statistical properties of the new methods are derived and finite sample properties are given. A financial and a medical application illustrate the use of the procedures.
Gelper, S. E. C., Schettlinger, K., Croux, C., & Gather, U. (2009). Robust online scale estimation in time series: A model-free approach. Journal of Statistical Planning and Inference, 139(2), 335-349. https://doi.org/10.1016/j.jspi.2008.04.018