I have got > 100 river daily flow time series and I need to select a threshold for each of them in order to perform a Peak Over Threshold extreme value analysis.

I know that I can select a threshold manually with specific R packages but I would like to know if there exists an automatic method which will calculate for me the most suitable threshold for each of the 100 time series.

e.g. I could set up a 90% threshold based on the max daily flow value but it could be a very extreme one and therefore I will miss all the other ones.

Any suggestion?



2 Answers 2


You should have a look to this article by C. Scarrott and A. Mac Donald A Review of Extreme Value Threshold Estimation and Uncertainty Quantification. A simple and reasonable idea is to combine two models: one for the bulk, one for the tail. At least, this makes the threshold choice less crucial than it is in standard POT. As you will see, some well-documented R packages on CRAN relate to the methods described in the article: evmix by C.J. Scarrott and Y. Hu and condmixt by J. Carreau.

Another reference is chap. 4 in the book Extreme Value Modeling and Risk Analysis.

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    $\begingroup$ @aaaaa It would be useful that you explain why you eventually 'unaccepted' this answer more than one year after it was written. $\endgroup$
    – Yves
    Sep 26, 2018 at 18:21

I suggest building a Transfer Function model (regression with steroids!) to predict daily values based upon memory and possible predictors like day-of-the-month , week-of-the-month , month-of-the-year et al . After forming a suitable model which of course would include possible intervention variables like pulses , level shifts , local time trends I would then forecast and obtain prediction intervals for each period in the future by re-sampling the model errors (allowing for anomalies in the future) and obtain a family of forecasts (frequency distributions) for each period out. I would then examine these monte-carlo distributions for their statistical properties (eg. max/min/median ) to assess threshold values. In this way you can manage your own analysis of the possible future values.

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    $\begingroup$ Seriously? You recommend modeling peak river flows in terms of human artifacts like days of the month and weeks of the month? (Maybe if the floods were entirely wastewater flows this could make some sense, but it's no place to begin such an analysis.) This answer looks like you posted your usual boilerplate response without even reading the question. $\endgroup$
    – whuber
    Mar 16, 2017 at 12:54
  • $\begingroup$ Au contraire there can be deterministic effects like month of the year and possible anomalous effects. I have seen research where monthly effects can be detected in hydrological studies. Certainly days-of-the-week might be suspect but not memory or predictor variables like the amount of rainfall. This absolutely was not a boiler-plate response with an attempt to introduce monte-carlo to generate a family of forecasts for each forecast period. $\endgroup$
    – IrishStat
    Mar 16, 2017 at 13:16
  • $\begingroup$ scholar.google.com/… is a reference that might be useful to understand , $\endgroup$
    – IrishStat
    Mar 16, 2017 at 13:27
  • $\begingroup$ If you would be so kind as to suggest a specific reference documenting your approach to POT analysis, rather than the myriad results of a generic search, I would be glad to look at it and retract my comments. $\endgroup$
    – whuber
    Mar 16, 2017 at 21:42
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    $\begingroup$ The point of that quotation is that whatever effects are identified in hydrological data tend (with only rare exceptions) to be driven by natural, not anthropogenic, phenomena. Thus one would never set out to include days of the week, weeks within individual calendar months, or the calendar months themselves as predictors in any meaningful model. One would instead look for seasonal terms within a water year and include covariates related to weather, climate, land use, and land cover. $\endgroup$
    – whuber
    Mar 17, 2017 at 14:23

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