function [alpha] = hillols(x, kfrac,sign)
% function alpha = hillols(x, kfrac, sign)
%     x = time series (univariate)
%     kfrac = fraction in tail (can be vector for comparison)
%     sign = +1 right, -1 left tail, 0 pool left and right
%     Returns: alpha  (the tail index) = 1/gamma (the shape parameter)
% 
%   Requires:  hill.m
% 
%      This code is based on the estimator developed in: 
%       Huisman, R., Koedijk, K. G., Kool, C. J. M. & Palm, F. (2001), 
%             Tail-index estimates in small samples, 
%             Journal of Business and Economic Statistics 19, pages 208-216
%


n = length(x);
% set range sizes - double for pooled tails
if (sign ~= 0)
    kvec = fix(kfrac*n);
else
    kvec = fix(2*kfrac*n);
end

h = zeros(length(kvec),1);

% first do hills
% set up recommended regression points at 5 to kvec
fullk = 5:1:kvec(end);
% now get vector of hills - this is costly, so do it once
h = hill(x,fullk,sign);

% Now implement the OLS part for each length
for j = 1:length(kvec)
    hreg = h(1:kvec(j)-4);
    kreg = 5:1:kvec(j);
    % weighting for WLS
    wt = sqrt(kreg);
    hreg = hreg.*wt;
    kx    = kreg.*wt;
    xx = [wt' kx'];
    % standard OLS estimator (this is WLS from wt weights)
    beta = inv(xx'*xx)*(xx'*hreg');
    % bias adjusted hill estimate is in constant term
    % estimate is for, gamma, the shape parameter
    % tail index (alpha) = 1/gamma
    alpha(j) = 1/beta(1);
end