Quantifying the Uncertainty around Break Dates in Step-Indicator Saturation

24 Pages Posted: 21 Apr 2023

See all articles by David F. Hendry

David F. Hendry

University of Oxford-Nuffield College

Felix Pretis

University of Victoria, Department of Economics; University of Oxford - Institute for New Economic Thinking at the Oxford Martin School

Date Written: April 11, 2023

Abstract

Quantifying the uncertainty around structural breaks is crucial to attribute breaks to potential causes. Step-Indicator saturation (SIS, see Castle et al 2015) allows for the detection of structural breaks using model selection, however, little is known about the uncertainty around the timing of detected breaks. Here we quantify the uncertainty around break dates in models selected using SIS, to help when attributing detected breaks to events. Relying on congruence of designed models in general-to-specific model selection, we use the approximate normal distribution of the error terms to compute the probability of the underlying break falling in any specified interval around a detected break. This allows us to compute approximate probabilities of the date of the true break indicator coinciding with the date of the estimated break indicator, as a function of the estimated break magnitude and error variance. This enables hypothesis tests on break dates - an invaluable feature when attributing detected shifts to known events, from shocks in economics, to policy interventions in climate change. Analytical results show that a two standard deviation shift precisely coincides with the correct date approximately 64% of the time, with an approximate 95% confidence interval of plus/minus 3 periods. Monte Carlo simulations confirm the approximate confidence intervals for the break date in SIS. We demonstrate our method for breaks in UK NOX emissions time series using the R-package `gets'.

Keywords: Structural break, date, uncertainty, step-indicator saturation, confidence interval

Suggested Citation

Hendry, David F. and Pretis, Felix, Quantifying the Uncertainty around Break Dates in Step-Indicator Saturation (April 11, 2023). Available at SSRN: https://ssrn.com/abstract=4416619 or http://dx.doi.org/10.2139/ssrn.4416619

David F. Hendry

University of Oxford-Nuffield College ( email )

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Oxford, OX1 1nf
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HOME PAGE: http://https://www.nuffield.ox.ac.uk/

Felix Pretis (Contact Author)

University of Victoria, Department of Economics ( email )

3800 Finnerty Rd
Victoria, British Columbia V8P 5C2
Canada

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

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Oxford, OX2 6ED
United Kingdom

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