Features

• 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

Improved fitting routine

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:

1. The user does not have to worry about the numerical optimization
   anymore. It will produce the correct results in nearly all cases.
2. The optimization itself becomes more robust and can now be used in
   an massive parallel setting.

Error estimates of the return level

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.

Better error handling

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.

Focused on handling time series

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.

Installation

In order to install this package, have two options.

Installation via GitLab

Via the devtools package

devtools::install_gitlab( "theGreatWhiteShark/climex" )

An interactive web application

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.

Features

• 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

Accessing station data

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.

Usage

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!

License

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