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## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: y = arch_rnd (a, b, T)
##
## Simulates an ARCH sequence y of length T with AR coefficients b and
## CH coefficients a.
## I.e., y follows the model
## y(t) = b(1) + b(2) * y(t-1) + ... + b(lb) * y(t-lb+1) + e(t),
## where e(t), given y up to time t-1, is N(0, h(t)), with
## h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(la) * e(t-la+1)^2.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Simulate an ARCH process
function y = arch_rnd (a, b, T)
if (nargin != 3)
usage ("arch_rnd (a, b, T)");
endif
if !( (min (size (a)) == 1) && (min (size (b)) == 1) )
error ("arch_rnd: a and b must both be scalars or vectors");
endif
if !( is_scalar (T) && (T > 0) && (rem (T, 1) == 0) )
error ("arch_rnd: T must be a positive integer");
endif
if !(a(1) > 0)
error ("arch_rnd: a(1) must be positive");
endif
## perhaps add a test for the roots of a(z) here ...
la = length (a);
a = reshape (a, 1, la);
if (la == 1)
a = [a, 0];
la = la + 1;
endif
lb = length (b);
b = reshape (b, 1, lb);
if (lb == 1)
b = [b, 0];
lb = lb + 1;
endif
M = max([la, lb]);
e = zeros (T, 1);
h = zeros (T, 1);
y = zeros (T, 1);
h(1) = a(1);
e(1) = sqrt (h(1)) * randn;
y(1) = b(1) + e(1);
for t= 2 : M;
ta = min ([t, la]);
h(t) = a(1) + a(2:ta) * e(t-1:t-ta+1).^2;
e(t) = sqrt (h(t)) * randn;
tb = min ([t, lb]);
y(t) = b(1) + b(2:tb) * y(t-1:t-tb+1) + e(t);
endfor
if (T > M)
for t = M+1 : T;
h(t) = a(1) + a(2:la) * e(t-1:t-la+1).^2;
e(t) = sqrt (h(t)) * randn;
y(t) = b(1) + b(2:lb) * y(t-1:t-tb+1) + e(t);
endfor
endif
y = y(1:T);
endfunction
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