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arch_rnd.m

## 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  = ;
    la = la + 1;
  endif
  lb = length (b);
  b  = reshape (b, 1, lb);
  if (lb == 1)
    b  = ;
    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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