- Improved fitting routine (no numerical artifacts like in other extreme value packages)
- Different methods, including statistical ones, to access the error estimates of arbitrary return levels and the upper limit extreme value distribution
- Better error handling allowing a massive parallel application
- Focuses on the handling of time series (xts instead of data.frame as its basic input class)
- A set of auxiliary functions frequently used in the extreme value analysis (EVA) of climate time series
The parameter estimation for the stationary generalized extreme value (GEV) and generalized Pareto (GP) distribution using unconstrained optimization (done by all other R packages involving extreme value statistics) tends to produce numerical artifacts. This is due to the presence of logarithms in the negative log-likelihood functions and a limited range of shape values the maximum likelihood estimators are defined in. While yielding absurdly large parameter values or causing the optimization to fail when using the BFGS algorithm (in the extRemes package), the differences using the Nelder-Mead algorithm (all other packages, e.g. ismev) might be small, barely noticeable, and totally plausible. But they are still present and spoil your calculation.
In order to avoid those numerical artifacts, the augmented Lagrangian method is used to incorporate both the logarithms and the limited range of shape values as non-linear constraints. With this approach the optimization can be started at arbitrary initial parameter combinations and will almost always converge to the global optimum. Only for initial parameter combinations chosen very badly the algorithm can still produce artifacts. But an improved version of the already quite decent heuristics for choosing them will prevent it.
This solves two remaining problems of the extreme value analysis:
- The user does not have to worry about the numerical optimization anymore. It will produce the correct results in nearly all cases.
- The optimization itself becomes more robust and can now be used in an massive parallel setting.
An important part of the extreme value analysis is to access the fitting errors introduced into the calculated return levels. The default way of obtaining them is to use the so-called delta method assuming normality of the log-likelihood function at the fitting result. This assumption, however, is not fulfilled in a lot of cases and is stronger violated the higher the shape parameter of the underlying GEV or GP distribution.
To nevertheless calculate a decent estimate of the fitting errors, the climex package introduces two statistical approaches, one based on bootstrap and the other one based on a Monte Carlo approach. In comparison to the calculation of the confidence intervals implemented in the extRemes package, the climex package calculates the standard deviation of the return levels. Since there are a lot of different sources of errors in the extreme value analysis, like too small block sizes, too low thresholds, or non-stationaries and/or correlations in the data, providing a confidence interval (CI) might the misleading for some users. All these additional errors are by no means included in the CI and have to be obtained in further studies to construct some appropriate CI of the calculated return levels.
Due to the use of either the Nelder-Mead or BFGS optimization algorithm, some time series will throw errors when fitted using the other R packages tailored for the extreme value analysis. When fitting 100 stations at once you can expect at least one of them to break your code.
In order to allow a massive parallel application of the extreme value analysis, the climex package features a more robust error handling. In addition, the improved fitting routine mentioned above is able to handle initial parameter combinations far more distant from the global optimum than feasible under any unconstrained routine.
The fundamental object class handled in the climex package is the time series class xts or lists of class xts objects. This allows the user to harness all the additional functions tailored for the analysis of time series, e.g. those of the lubridate package. It also includes a couple of convenience functions often used within the extreme value analysis, like blocking, application of a threshold, declustering, deseasonalization etc.
In order to install this package, have two options.
Via the devtools package
devtools::install_gitlab( "theGreatWhiteShark/climex" )A convenient interface to this core package can be found in the climexUI package. It comes with a full-fledged shiny application, which enables the user to access and investigate a lot of different station data and, at the same time, to tweak the most important parameters involved in the preprocessing and the fitting procedure of the GEV or GP distribution.
- You can perform extreme value analysis on a large number of climatic time series from different stations
- You can calculate arbitrary return levels for all stations and display the results comprehensively on a map
- You have full control over all steps involved in the extreme value analysis of the station data via an intuitive GUI in a persistent way (changes will be applied to the analysis of all following time series)
- The fitting of both the GEV and the GP distribution is supported
- You can exclude single points or whole parts of a time series with the entire analysis updated immediately
- The fitting is done using a non-linear constrained maximum likelihood procedure based on the augmented Lagrangian method. Using this approach none of your fits will produce numerical artifacts
If you are at the very beginning of your analysis or still in search of a vast data base to perform your analysis on, I recommend you to check out the dwd2r package. It is capable of formatting and saving the station data provided by the German weather service (DWD) in lists of xts class objects and thus in the format most natural to work with in the context of the climex package.
You are new to R? Then check out the compiled list of resources from RStudio or the official introduction.
A thorough introduction is provided for the general usage of the package.
When using this package in your own analysis, keep in mind that its functions expect your time series to be of class xts and not numeric!
This package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License, version 3, as published by the Free Software Foundation.
This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.
A copy of the GNU General Public License, version 3, is available at http://www.r-project.org/Licenses/GPL-3