Mercurial > octave
annotate scripts/signal/arch_rnd.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 28 Dec 2021 18:22:40 -0500 |
| parents | 7854d5752dd2 |
| children | 5d3faba0342e |
| rev | line source |
|---|---|
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 1995-2022 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
| 3426 | 7 ## |
| 3922 | 8 ## This file is part of Octave. |
| 9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
| 3922 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
| 3426 | 14 ## |
| 3922 | 15 ## Octave is distributed in the hope that it will be useful, but |
| 3191 | 16 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
| 3426 | 19 ## |
| 3191 | 20 ## You should have received a copy of the GNU General Public License |
| 7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
| 3191 | 25 |
| 3449 | 26 ## -*- texinfo -*- |
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27 ## @deftypefn {} {} arch_rnd (@var{a}, @var{b}, @var{t}) |
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28 ## Simulate an ARCH sequence of length @var{t} with AR coefficients @var{b} and |
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29 ## CH coefficients @var{a}. |
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30 ## |
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31 ## The result @math{y(t)} follows the model |
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32 ## @c Set example in small font to prevent overfull line |
| 3191 | 33 ## |
| 7031 | 34 ## @smallexample |
| 3499 | 35 ## y(t) = b(1) + b(2) * y(t-1) + @dots{} + b(lb) * y(t-lb+1) + e(t), |
| 7031 | 36 ## @end smallexample |
| 3449 | 37 ## |
| 38 ## @noindent | |
| 3499 | 39 ## where @math{e(t)}, given @var{y} up to time @math{t-1}, is |
| 40 ## @math{N(0, h(t))}, with | |
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41 ## @c Set example in small font to prevent overfull line |
| 3449 | 42 ## |
| 7031 | 43 ## @smallexample |
| 3499 | 44 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(la) * e(t-la+1)^2 |
| 7031 | 45 ## @end smallexample |
| 3449 | 46 ## @end deftypefn |
| 3191 | 47 |
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48 function y = arch_rnd (a, b, t) |
| 3426 | 49 |
| 3191 | 50 if (nargin != 3) |
| 6046 | 51 print_usage (); |
| 3191 | 52 endif |
| 3426 | 53 |
| 3457 | 54 if (! ((min (size (a)) == 1) && (min (size (b)) == 1))) |
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55 error ("arch_rnd: A and B must both be scalars or vectors"); |
| 3191 | 56 endif |
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57 if (! (isscalar (t) && (t > 0) && (rem (t, 1) == 0))) |
| 3457 | 58 error ("arch_rnd: T must be a positive integer"); |
| 3191 | 59 endif |
| 3426 | 60 |
| 3457 | 61 if (! (a(1) > 0)) |
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62 error ("arch_rnd: A(1) must be positive"); |
| 3191 | 63 endif |
| 64 ## perhaps add a test for the roots of a(z) here ... | |
| 3426 | 65 |
| 3191 | 66 la = length (a); |
| 67 a = reshape (a, 1, la); | |
| 68 if (la == 1) | |
| 69 a = [a, 0]; | |
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70 la += 1; |
| 3191 | 71 endif |
| 7436 | 72 |
| 3191 | 73 lb = length (b); |
| 74 b = reshape (b, 1, lb); | |
| 75 if (lb == 1) | |
| 76 b = [b, 0]; | |
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77 lb += 1; |
| 3191 | 78 endif |
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79 m = max ([la, lb]); |
| 3426 | 80 |
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81 e = zeros (t, 1); |
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82 h = zeros (t, 1); |
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83 y = zeros (t, 1); |
| 3426 | 84 |
| 3191 | 85 h(1) = a(1); |
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86 e(1) = sqrt (h(1)) * randn (); |
| 3191 | 87 y(1) = b(1) + e(1); |
| 3426 | 88 |
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89 for t = 2:m |
| 3238 | 90 ta = min ([t, la]); |
| 7436 | 91 h(t) = a(1) + a(2:ta) * e(t-ta+1:t-1).^2; |
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92 e(t) = sqrt (h(t)) * randn (); |
| 3238 | 93 tb = min ([t, lb]); |
| 7436 | 94 y(t) = b(1) + b(2:tb) * y(t-tb+1:t-1) + e(t); |
| 3191 | 95 endfor |
| 7436 | 96 |
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97 if (t > m) |
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98 for t = m+1:t |
| 7436 | 99 h(t) = a(1) + a(2:la) * e(t-la+1:t-1).^2; |
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100 e(t) = sqrt (h(t)) * randn (); |
| 7436 | 101 y(t) = b(1) + b(2:lb) * y(t-tb+1:t-1) + e(t); |
| 3191 | 102 endfor |
| 103 endif | |
| 3426 | 104 |
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105 y = y(1:t); |
| 3426 | 106 |
| 3191 | 107 endfunction |