Mercurial > octave
annotate scripts/signal/arch_rnd.m @ 22323:bac0d6f07a3e
maint: Update copyright notices for 2016.
| author | John W. Eaton <jwe@octave.org> |
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| date | Wed, 17 Aug 2016 01:05:19 -0400 |
| parents | 516bb87ea72e |
| children | 3a2b891d0b33 e9a0469dedd9 |
| rev | line source |
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1 ## Copyright (C) 1995-2016 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3191 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3191 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3191 | 18 |
| 3449 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {} {} arch_rnd (@var{a}, @var{b}, @var{t}) |
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21 ## Simulate an ARCH sequence of length @var{t} with AR coefficients @var{b} and |
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22 ## CH coefficients @var{a}. |
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23 ## |
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24 ## The result @math{y(t)} follows the model |
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25 ## @c Set example in small font to prevent overfull line |
| 3191 | 26 ## |
| 7031 | 27 ## @smallexample |
| 3499 | 28 ## y(t) = b(1) + b(2) * y(t-1) + @dots{} + b(lb) * y(t-lb+1) + e(t), |
| 7031 | 29 ## @end smallexample |
| 3449 | 30 ## |
| 31 ## @noindent | |
| 3499 | 32 ## where @math{e(t)}, given @var{y} up to time @math{t-1}, is |
| 33 ## @math{N(0, h(t))}, with | |
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34 ## @c Set example in small font to prevent overfull line |
| 3449 | 35 ## |
| 7031 | 36 ## @smallexample |
| 3499 | 37 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(la) * e(t-la+1)^2 |
| 7031 | 38 ## @end smallexample |
| 3449 | 39 ## @end deftypefn |
| 3191 | 40 |
| 5428 | 41 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3457 | 42 ## Description: Simulate an ARCH process |
| 3191 | 43 |
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44 function y = arch_rnd (a, b, t) |
| 3426 | 45 |
| 3191 | 46 if (nargin != 3) |
| 6046 | 47 print_usage (); |
| 3191 | 48 endif |
| 3426 | 49 |
| 3457 | 50 if (! ((min (size (a)) == 1) && (min (size (b)) == 1))) |
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51 error ("arch_rnd: A and B must both be scalars or vectors"); |
| 3191 | 52 endif |
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53 if (! (isscalar (t) && (t > 0) && (rem (t, 1) == 0))) |
| 3457 | 54 error ("arch_rnd: T must be a positive integer"); |
| 3191 | 55 endif |
| 3426 | 56 |
| 3457 | 57 if (! (a(1) > 0)) |
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58 error ("arch_rnd: A(1) must be positive"); |
| 3191 | 59 endif |
| 60 ## perhaps add a test for the roots of a(z) here ... | |
| 3426 | 61 |
| 3191 | 62 la = length (a); |
| 63 a = reshape (a, 1, la); | |
| 64 if (la == 1) | |
| 65 a = [a, 0]; | |
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66 la += 1; |
| 3191 | 67 endif |
| 7436 | 68 |
| 3191 | 69 lb = length (b); |
| 70 b = reshape (b, 1, lb); | |
| 71 if (lb == 1) | |
| 72 b = [b, 0]; | |
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73 lb += 1; |
| 3191 | 74 endif |
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75 m = max ([la, lb]); |
| 3426 | 76 |
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77 e = zeros (t, 1); |
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78 h = zeros (t, 1); |
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79 y = zeros (t, 1); |
| 3426 | 80 |
| 3191 | 81 h(1) = a(1); |
| 82 e(1) = sqrt (h(1)) * randn; | |
| 83 y(1) = b(1) + e(1); | |
| 3426 | 84 |
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85 for t = 2:m |
| 3238 | 86 ta = min ([t, la]); |
| 7436 | 87 h(t) = a(1) + a(2:ta) * e(t-ta+1:t-1).^2; |
| 3191 | 88 e(t) = sqrt (h(t)) * randn; |
| 3238 | 89 tb = min ([t, lb]); |
| 7436 | 90 y(t) = b(1) + b(2:tb) * y(t-tb+1:t-1) + e(t); |
| 3191 | 91 endfor |
| 7436 | 92 |
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93 if (t > m) |
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94 for t = m+1:t |
| 7436 | 95 h(t) = a(1) + a(2:la) * e(t-la+1:t-1).^2; |
| 3191 | 96 e(t) = sqrt (h(t)) * randn; |
| 7436 | 97 y(t) = b(1) + b(2:lb) * y(t-tb+1:t-1) + e(t); |
| 3191 | 98 endfor |
| 99 endif | |
| 3426 | 100 |
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101 y = y(1:t); |
| 3426 | 102 |
| 3191 | 103 endfunction |
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104 |