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(pu) model for whether a given observation exceeds the threshold u.
2. A generalised Pareto, GP(σu,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 (pu,σu,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.