HILLGEV Procedure

@HILLGEV estimates the tail index of a distribution using Hill's(1975) method.

@HillGEV( options ) series start end

Parameters

series	series to analyze
start, end	range of series to use. By default, the defined range of series.

Options

TAIL=[LEFT]/RIGHT

Selects which tail to analyze.

ORDER/[NOORDER]

Use ORDER if the series is not already sorted (in increasing order). If you're doing the estimates for more than one span, it's a good idea to sort (a copy of) the series first.

SPAN=number of extreme observations used [10% of number of data points]

SMPL=standard SMPL option [not used]

Variables Defined

%%HILL	estimate of the tail index (REAL)
%%HILLSE	estimate of the standard error for %%HILL (REAL)

Example

This shows calculation of the tail index (for each tail) using the 190 most extreme values. (The full example analyzes different values for SPAN). This is from one of the Tsay textbook examples.

* Tsay, Analysis of Financial Time Series, 3rd edition

* Example 7.5.3 from pp 348-353

open data d-ibmln98.dat

data(format=free,org=columns) 1 9190 ibmlog

mvstats(min=mins,max=maxs,span=21) ibmlog

sample(smpl=%clock(t,21)==21) mins / mincomp

sample(smpl=%clock(t,21)==21) maxs / maxcomp

spgraph(footer="Figure 7.3 Maximum and minimum daily log returns (subperiod=21 days)",vfields=2)

graph(header="(a) Monthly maximum log returns")

# maxcomp

graph(header="(b) Monthly minimum log returns")

# mincomp

spgraph(done)

* Create a sorted version of ibmlog. (Most of the time computing Hill's

* estimate is spent sorting the data set).

set sorted = ibmlog

order sorted

report(action=define)

report(atrow=1,atcol=1,fillby=cols) "q" "Maximum" "Minimum"

report(atrow=1,atcol=2,tocol=3,span,align=center) "190"

@HillGEV(span=190,tail=right) sorted

report(atrow=2,atcol=2) %%hill %%hillse

@HillGEV(span=190,tail=left) sorted

report(atrow=3,atcol=2) %%hill %%hillse