|
3191
|
1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
|
|
2 ## |
|
|
3 ## This program is free software; you can redistribute it and/or modify |
|
|
4 ## it under the terms of the GNU General Public License as published by |
|
|
5 ## the Free Software Foundation; either version 2, or (at your option) |
|
|
6 ## any later version. |
|
|
7 ## |
|
|
8 ## This program is distributed in the hope that it will be useful, but |
|
|
9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
|
|
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|
|
11 ## General Public License for more details. |
|
|
12 ## |
|
|
13 ## You should have received a copy of the GNU General Public License |
|
|
14 ## along with this file. If not, write to the Free Software Foundation, |
|
|
15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
|
|
16 |
|
|
17 ## usage: y = arch_rnd (a, b, T) |
|
|
18 ## |
|
|
19 ## Simulates an ARCH sequence y of length T with AR coefficients b and |
|
|
20 ## CH coefficients a. |
|
|
21 ## I.e., y follows the model |
|
|
22 ## y(t) = b(1) + b(2) * y(t-1) + ... + b(lb) * y(t-lb+1) + e(t), |
|
|
23 ## where e(t), given y up to time t-1, is N(0, h(t)), with |
|
|
24 ## h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(la) * e(t-la+1)^2. |
|
|
25 |
|
|
26 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
|
|
27 ## Description: Simulate an ARCH process |
|
|
28 |
|
|
29 function y = arch_rnd (a, b, T) |
|
|
30 |
|
|
31 if (nargin != 3) |
|
|
32 usage ("arch_rnd (a, b, T)"); |
|
|
33 endif |
|
|
34 |
|
|
35 if !( (min (size (a)) == 1) && (min (size (b)) == 1) ) |
|
|
36 error ("arch_rnd: a and b must both be scalars or vectors"); |
|
|
37 endif |
|
|
38 if !( is_scalar (T) && (T > 0) && (rem (T, 1) == 0) ) |
|
|
39 error ("arch_rnd: T must be a positive integer"); |
|
|
40 endif |
|
|
41 |
|
|
42 if !(a(1) > 0) |
|
|
43 error ("arch_rnd: a(1) must be positive"); |
|
|
44 endif |
|
|
45 ## perhaps add a test for the roots of a(z) here ... |
|
|
46 |
|
|
47 la = length (a); |
|
|
48 a = reshape (a, 1, la); |
|
|
49 if (la == 1) |
|
|
50 a = [a, 0]; |
|
|
51 la = la + 1; |
|
|
52 endif |
|
|
53 lb = length (b); |
|
|
54 b = reshape (b, 1, lb); |
|
|
55 if (lb == 1) |
|
|
56 b = [b, 0]; |
|
|
57 lb = lb + 1; |
|
|
58 endif |
|
3238
|
59 M = max([la, lb]); |
|
3191
|
60 |
|
|
61 e = zeros (T, 1); |
|
|
62 h = zeros (T, 1); |
|
|
63 y = zeros (T, 1); |
|
|
64 |
|
|
65 h(1) = a(1); |
|
|
66 e(1) = sqrt (h(1)) * randn; |
|
|
67 y(1) = b(1) + e(1); |
|
|
68 |
|
|
69 for t= 2 : M; |
|
3238
|
70 ta = min ([t, la]); |
|
3191
|
71 h(t) = a(1) + a(2:ta) * e(t-1:t-ta+1).^2; |
|
|
72 e(t) = sqrt (h(t)) * randn; |
|
3238
|
73 tb = min ([t, lb]); |
|
3191
|
74 y(t) = b(1) + b(2:tb) * y(t-1:t-tb+1) + e(t); |
|
|
75 endfor |
|
|
76 if (T > M) |
|
|
77 for t = M+1 : T; |
|
|
78 h(t) = a(1) + a(2:la) * e(t-1:t-la+1).^2; |
|
|
79 e(t) = sqrt (h(t)) * randn; |
|
|
80 y(t) = b(1) + b(2:lb) * y(t-1:t-tb+1) + e(t); |
|
|
81 endfor |
|
|
82 endif |
|
|
83 |
|
|
84 y = y(1:T); |
|
|
85 |
|
|
86 endfunction |
|
|
87 |
