lite: Likelihood-Based Inference for Time Series Extremes version 1.1.1

lite 1.1.1

Bug fixes and minor improvements

• Fixed 2 \link{} targets with missing (exdex) package anchors in Rd files for blite() and flite()

lite: Likelihood-Based Inference for Time Series Extremes version 1.1.0

lite 1.1.0

New features

• The new function blite() performs Bayesian threshold-based inference for time series extremes. It is a Bayesian version of the existing function flite(), which performs frequentist inference.

• Objects returned from blite() have a predict S3 method predict.blite() based on the predict.evpost() method from the revdbayespackage. It provides predictive inferences for the largest value observed in N years.

• Objects of class flite returned from flite() now have a confint method.

Bug fixes and minor improvements

• In flite(), the arguments k and inc_cens were not passed to exdex::kgaps(). This has been corrected.

• In the (unexported, internal) function bingp_rl_CI() an error is triggered if the return level requested is lower than the threshold used to fit the model.

• In the (unexported, internal) function bingp_rl_prof(), which calculates a confidence interval for a return level based on a profile log-likelihood, a check is made on the value p to be passed to revdbayes::qgp() to check that it is in [0, 1].

lite: Likelihood-Based Inference for Time Series Extremes

lite

Likelihood-Based Inference for Time Series Extremes

The lite package performs likelihood-based inference for stationary time series extremes. The general approach follows Fawcett and Walshaw (2012). There are 3 independent parts to the inference, all performed using maximum likelihood estimation.

1. A Bernoulli(p_u) model for whether a given observation exceeds the threshold u.
2. A generalised Pareto, GP(σ_u,ξ), model for the marginal distribution of threshold excesses.
3. The K-gaps model for the extremal index θ, based on inter-exceedance times.

For parts 1 and 2 it is necessary to adjust the inferences because we expect that the data will exhibit cluster dependence. This is achieved using the methodology developed in Chandler and Bate (2007) to produce a log-likelihood that is adjusted for this dependence. This is achieved using the chandwich package. For part 3, the methodology described in Süveges and Davison (2010) is used, implemented by the function kgaps in the exdex package. The (adjusted) log-likelihoods from parts 1, 2 and 3 are combined to make inferences about return levels.

An example: Cheeseboro wind gusts

The function flite makes inferences about (p_u,σ_u,ξ,θ). We illustrate this using the cheeseboro data from the exdex package, which contains hourly wind gust data from each January over the 10-year period 2000-2009.

First, we make inferences about the model parameters.

library(lite)
cdata <- exdex::cheeseboro
# Each column of the matrix cdata corresponds to data from a different year
# flite() sets cluster automatically to correspond to column (year)
cfit <- flite(cdata, u = 45, k = 3)

Then, we make inferences about the 100-year return level, including 95% confidence intervals. The argument ny sets the number of observations per year, which is 31 × 24 = 744 for these data.

rl <- returnLevel(cfit, m = 100, level = 0.95, ny = 31 * 24)
rl
#> 
#> Call:
#> returnLevel(x = cfit, m = 100, level = 0.95, ny = 31 * 24)
#> 
#> MLE and 95% confidence limits for the 100-year return level
#> 
#> Normal interval:
#>  lower     mle   upper  
#>  70.36   90.73  111.09  
#> Profile likelihood-based interval:
#>  lower     mle   upper  
#>  77.29   90.73  132.57

Installation

To get the current released version from CRAN:

install.packages("lite")

Vignette

See vignette("introduction-to-lite", package = "lite") for an overview of the package.