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Statistical Modeling of Stochastic Level Shifts in Time Series

Thomas M. Trimbur(1)


Methods are developed for estimating trends in time series subject to level shifts. The approach is based on specifying stochastic models for breaks as part of the model structure, using heavy-tailed densities to allow for a positive probability of such a large change at any given time. Examining changes in trend movements, estimated from the dynamics of the dataset, provides more information than a yes/no criterion for making decisions on level shift events. Continuous-valued innovations in the trend are assessed using a statistical model; with the arrival of a data point that constitutes a break, timely warning is given with a smooth shift in the assessment. The empirical illustrations show how more robust trend estimates are obtained in practice.


Level shifts, Unobserved components, Heavy-tailed density, Non-Gaussian model, Robustness, Trend estimation of shifts.

(1) Thomas M. Trimbur is currently at the U. S. Federal Reserve Board email :

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: April 02, 2015