How to Describe and Propagate Uncertainty When Processing Time Series: Metrological and Computational Challenges, with Potential Applications to Environmental Studies

Authors

Christian Servin, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow
Aline Jaimes, The University of Texas at El PasoFollow
Craig Tweedie, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-2012

Comments

Technical Report: UTEP-CS-12-01a

Published in: Shyi-Ming Chen and and Witold Pedrycz (eds.), Time Series Analysis, Modeling and Applications: A Computational Intelligence Perspective, Springer Verlag, 2013, pp. 279-299.

Abstract

Time series comes from measurements, and measurements are never absolutely accurate. Traditionally, when we deal with an individual measurement or with a sample of measurement results, we subdivide a measurement error into random and systematic components: systematic error does not change from measurement to measurement which random errors corresponding to different measurements are independent. In time series, when we measure the same quantity at different times, we can also have correlation between measurement errors corresponding to nearby moments of time. To capture this correlation, environmental science researchers proposed to consider the third type of measurement errors: periodic. This extended classification of measurement error may seem ad hoc at first glance, but it leads to a good description of the actual errors. In this paper, we provide a theoretical explanation for this semi-empirical classification, and we show how to efficiently propagate all types of uncertainty via computations.