dgaps_imt

Performs an information matrix test (IMT) to diagnose misspecification of
the \(D\)-gaps model of Holesovsky and Fusek (2020).

Performs frequentist inference for the extremal index of a
stationary time series. Two types of methodology are used. One type is
based on a model that relates the distribution of block maxima to the
marginal distribution of series and leads to the semiparametric maxima
estimators described in Northrop (2015) <doi:10.1007/s10687-015-0221-5> and
Berghaus and Bucher (2018) <doi:10.1214/17-AOS1621>. Sliding block maxima
are used to increase precision of estimation. A graphical block size
diagnostic is provided. The other type of methodology uses a model for the
distribution of threshold inter-exceedance times (Ferro and Segers (2003)
<doi:10.1111/1467-9868.00401>). Three versions of this type of approach are
provided: the iterated weight least squares approach of Suveges (2007)
<doi:10.1007/s10687-007-0034-2>, the K-gaps model of
Suveges and Davison (2010) <doi:10.1214/09-AOAS292> and a similar approach
of Holesovsky and Fusek (2020) <doi:10.1007/s10687-020-00374-3>
that we refer to as D-gaps. For the K-gaps and D-gaps models this package
allows missing values in the data, can accommodate independent subsets of
data, such as monthly or seasonal time series from different years, and can
incorporate information from right-censored inter-exceedance times.
Graphical diagnostics for the threshold level and the respective tuning
parameters K and D are provided.

Paul Northrop

exdex

Estimation of the Extremal Index

Constantinos Christodoulides

dgaps_imt function

<dl><dt>data</dt>
<dd>A numeric vector or numeric matrix of raw data. If <code>data</code>
 is a matrix then the log-likelihood is constructed as the sum of
 (independent) contributions from different columns. A common situation is
 where each column relates to a different year.
If <code>data</code> contains missing values then <code>split_by_NAs</code> is
 used to divide the data into sequences of non-missing values.</dd>
<dt>u, D</dt>
<dd>Numeric vectors. <code>u</code> is a vector of extreme value
 thresholds applied to data. <code>D</code> is a vector of values of the
 left-censoring parameter \(D\), as defined in Holesovsky and Fusek
 (2020). See <code>dgaps</code>.
Any values in <code>u</code> that are greater than all the observations in
 <code>data</code> will be removed without a warning being given.</dd>
<dt>inc_cens</dt>
<dd>A logical scalar indicating whether or not to include
contributions from right-censored inter-exceedance times, relating to the
first and last observations. See <code>dgaps</code>.</dd></dl>

Arguments

Information matrix test under the \(D\)-gaps model — dgaps_imt

<dl>

<dt>data</dt>
<dd>A numeric vector or numeric matrix of raw data. If <code>data</code>
 is a matrix then the log-likelihood is constructed as the sum of
 (independent) contributions from different columns. A common situation is
 where each column relates to a different year.
If <code>data</code> contains missing values then <code>split_by_NAs</code> is
 used to divide the data into sequences of non-missing values.</dd>


<dt>u, D</dt>
<dd>Numeric vectors. <code>u</code> is a vector of extreme value
 thresholds applied to data. <code>D</code> is a vector of values of the
 left-censoring parameter \(D\), as defined in Holesovsky and Fusek
 (2020). See <code>dgaps</code>.
Any values in <code>u</code> that are greater than all the observations in
 <code>data</code> will be removed without a warning being given.</dd>


<dt>inc_cens</dt>
<dd>A logical scalar indicating whether or not to include
contributions from right-censored inter-exceedance times, relating to the
first and last observations. See <code>dgaps</code>.</dd>

</dl>

dgaps_imt: Information matrix test under the \(D\)-gaps model

Description

Usage

Value

Arguments

Details

References

See Also

Examples