Abstract
The paper considers the nature of stationarity of a time series or signal, and how it may be quantified. It is argued that a subjective assessment is as effective as one based on mathematical definitions, if one actually has finite samples of data, and that such an assessment is fundamentally based on the number of cycles of the dominant periodic component visible in the sample. It is shown by dimensional analysis that one of the most often-used measures of stationarity – the Augmented Dickey-Fuller (ADF) statistic – supports this hypothesis. The paper should be of interest not just to engineers, but also to econometricians, or anyone concerned with time series analysis and the impact of nonstationarity.
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Notes
- 1.
Things are a little more complicated than this, detection using a control chart depends critically on the tails of the signal probability density, and these are independent/insensitive to the central statistics controlled in weak stationarity.
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KW would like to acknowledge the support of the UK Engineering and Physical Sciences Research Council (EPSRC) through grant reference numbers EP/J016942/1 and EP/K003836/2.
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Worden, K., Iakovidis, I., Cross, E.J. (2019). On Stationarity and the Interpretation of the ADF Statistic. In: Pakzad, S. (eds) Dynamics of Civil Structures, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-74421-6_5
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