# 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.

- A Bernoulli(
*p*_{u}) model for whether a
given observation exceeds the threshold *u*.
- A generalised Pareto,
GP(
*σ*_{u},*ξ*), model for the marginal
distribution of threshold excesses.
- 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:

### Vignette

See `vignette("introduction-to-lite", package = "lite")`

for an overview of the package.