alpha_hill

Computes the estimator of the tail index proposed by Hill (1975).

Companion package of Carrion-i-Silvestre & Sansó (2023):
"Generalized Extreme Value Approximation to the CUMSUMQ Test for Constant
Unconditional Variance in Heavy-Tailed Time Series". It implements the Modified
Iterative Cumulative Sum of Squares Algorithm, which is an extension of
the Iterative Cumulative Sum of Squares (ICSS) Algorithm of Inclan and Tiao (1994), and it checks for changes in the
unconditional variance of a time series controlling for the tail index of
the underlying distribution. The fourth order moment is estimated non-parametrically
to avoid the size problems when the innovations are non-Gaussian (see, Sansó et al., 2004).
Critical values and p-values are generated using a Generalized Extreme Value distribution approach.
References
Carrion-i-Silvestre J.J & Sansó A (2023) <https://www.ub.edu/irea/working_papers/2023/202309.pdf>.
Inclan C & Tiao G.C (1994) <doi:10.1080/01621459.1994.10476824>,
Sansó A & Aragó V & Carrion-i-Silvestre J.L (2004) <https://dspace.uib.es/xmlui/bitstream/handle/11201/152078/524035.pdf>.

Andreu Sansó

micss

Modified Iterative Cumulative Sum of Squares Algorithm

Josep Lluís Carrion-i-Silvestre

alpha_hill function

<dl><dt>x</dt>
<dd>A numeric vector.</dd><dt>k</dt>
<dd>Fraction of the upper tail to be used to estimate of the tail index.</dd></dl>

Arguments

Hill's estimator of the tail index — alpha_hill

<dl>

<dt>x</dt>
<dd>A numeric vector.</dd>

<dt>k</dt>
<dd>Fraction of the upper tail to be used to estimate of the tail index.</dd>

</dl>

alpha_hill: Hill's estimator of the tail index

Description

Usage

Value

Arguments

References

See Also

Examples