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Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis

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Abstract

River flow data are usually subject to several sources of discontinuity and inhomogeneity. An example is seasonality, because climatic oscillations occurring on inter-annual timescale have an obvious impact on the river flow. Further sources of alteration can be caused by changes in reservoir management, instrumentation or even unexpected shifts in climatic conditions. When such changes are ignored the results of a statistical analysis can be strongly misleading, so flexible procedures are needed for building the appropriate models, which may be very complex. This paper develops an automatic procedure to estimate the number and locations of changepoints in Periodic AutoRegressive (PAR) models, which have been extensively used to account for seasonality in hydrology. We aim at filling the literature gap on multiple changepoint detection by allowing several time segments to be detected, inside of which a different PAR structure is specified, with the resulting model being employed to successfully capture the discontinuities of river flow data. The model estimation is performed by optimization of an objective function based on an information criterion using genetic algorithms. The proposed methodology is evaluated by means of simulation studies and it is then employed in the analysis of two river flows: the South Saskatchewan, measured at Saskatoon, Canada, and the Colorado, measured at Lees Ferry, Arizona. For these river flows we build changepoint models, discussing the possible events that caused discontinuity, and evaluate their forecasting accuracy. Comparisons with the literature on river flow analysis and on existing methods for changepoint detection confirm the efficiency of our proposal.

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Source: South East Alberta Watershed Alliance

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Source: U.S. department of the interior

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Notes

  1. Source: http://www.stats.uwo.ca/faculty/mcleod/epubs/mhsets/readme-mhsets.html.

  2. Source: https://www.usbr.gov/lc/region/g4000/NaturalFlow/current.html.

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Acknowledgements

The authors wish to thank Francesco Battaglia for his valuable and constructive remarks, QiQi Lu for providing us with the Fortran code related to the algorithm in Lu et al. (2010) and several anonymous referees for their useful comments. Part of this work has been carried out with the financial support of the CNRS and the French National Research Agency (ANR) in the framework of the Investments for the Future Program, within the Cluster of Excellence COTE (ANR-10-LABX-45).

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Authors and Affiliations

  1. Department of Economics and Statistics, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, Italy

    Domenico Cucina

  2. Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00100, Rome, Italy

    Manuel Rizzo

  3. GREThA UMR-CNRS 5113, Université de Bordeaux, Avenue Léon Duguit, 33608, Pessac Cedex, France

    Eugen Ursu

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  1. Domenico Cucina
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Correspondence to Manuel Rizzo.

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Cucina, D., Rizzo, M. & Ursu, E. Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis. Stoch Environ Res Risk Assess 33, 1137–1157 (2019). https://doi.org/10.1007/s00477-019-01692-0

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