The extremal index *θ* is a measure of the degree of local
dependence in the extremes of a stationary process. The
`exdex`

package performs frequentist inference about
*θ* using two types of methodology.

One type (Northrop, 2015) is based on a model that relates the distribution of block maxima to the marginal distribution of the data, leading to a semiparametric maxima estimator. Two versions of this type of estimator are provided, following Northrop, 2015 and Berghaus and Bücher, 2018. A slightly modified version of the latter is also provided. Estimates are produced using both disjoint and sliding block maxima, the latter providing greater 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). Two versions of this type of approach are provided: the
iterated weight least squares approach of Süveges (2007) and
the *K*-gaps model of Süveges and Davison
(2010). For the *K*-gaps model the `exdex`

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 censored interexceedance times. A
graphical diagnostic for the threshold level and the runs parameter
*K* is provided.

The following code estimates the extremal index using the
semiparametric maxima estimators, for an example dataset containing a
time series of sea surges measured at Newlyn, Cornwall, UK over the
period 1971-1976. The block size of 20 was chosen using a graphical
diagnostic provided by `choose_b()`

.

```
library(exdex)
<- spm(newlyn, 20)
theta
theta#>
#> Call:
#> spm(data = newlyn, b = 20)
#>
#> Estimates of the extremal index theta:
#> N2015 BB2018 BB2018b
#> sliding 0.2392 0.3078 0.2578
#> disjoint 0.2350 0.3042 0.2542
summary(theta)
#>
#> Call:
#> spm(data = newlyn, b = 20)
#>
#> Estimate Std. Error Bias adj.
#> N2015, sliding 0.2392 0.01990 0.003317
#> BB2018, sliding 0.3078 0.01642 0.003026
#> BB2018b, sliding 0.2578 0.01642 0.053030
#> N2015, disjoint 0.2350 0.02222 0.003726
#> BB2018, disjoint 0.3042 0.02101 0.003571
#> BB2018b, disjoint 0.2542 0.02101 0.053570
```

Now we estimate *θ* using the *K*-gaps model. The
threshold *u* and runs parameter *K* were chosen using the
graphical diagnostic provided by `choose_uk()`

.

```
<- quantile(newlyn, probs = 0.60)
u <- kgaps(newlyn, u, k = 2)
theta
theta#>
#> Call:
#> kgaps(data = newlyn, u = u, k = 2)
#>
#> Estimate of the extremal index theta:
#> [1] 0.1758
summary(theta)
#>
#> Call:
#> kgaps(data = newlyn, u = u, k = 2)
#>
#> Estimate Std. Error
#> theta 0.1758 0.009211
```

To get the current released version from CRAN:

`install.packages("exdex")`

See `vignette("exdex-vignette", package = "exdex")`

for an
overview of the package.