MomTailIndex {ExtremeRisks} R Documentation

## Moment based Tail Index Estimation

### Description

Computes a point estimate of the tail index based on the Moment Based (MB) estimator.

### Usage

```MomTailIndex(data, k)
```

### Arguments

 `data` A vector of (1 x n) observations. `k` An integer specifying the value of the intermediate sequence k_n. See Details.

### Details

For a dataset `data` of sample size n, the tail index γ of its (marginal) distribution is computed by applying the MB estimator. The observations can be either independent or temporal dependent. For details see de Haan and Ferreira (2006).

• `k` or k_n is the value of the so-called intermediate sequence k_n, n=1,2,.... Its represents a sequence of positive integers such that k_n -> ∞ and k_n/n -> 0 as n -> ∞. Practically, the value k_n specifies the number of `k`+1 larger order statistics to be used to estimate γ.

### Value

An estimate of the tail index γ.

### References

de Haan, L. and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer-Verlag, New York.

### Examples

```# Tail index estimation based on the Moment estimator obtained with
# 1-dimensional data simulated from an AR(1) with univariate Student-t
# distributed innovations

tsDist <- "studentT"
tsType <- "AR"

# parameter setting
corr <- 0.8
df <- 3
par <- c(corr, df)

# Big- small-blocks setting
bigBlock <- 65
smallblock <- 15

# Number of larger order statistics
k <- 150

# sample size
ndata <- 2500

# Simulates a sample from an AR(1) model with Student-t innovations
data <- rtimeseries(ndata, tsDist, tsType, par)

# tail index estimation
gammaHat <- MomTailIndex(data, k)
gammaHat
```

[Package ExtremeRisks version 0.0.4 Index]