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1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2003, 2005, 2006, |
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2 ## 2007 Friedrich Leisch |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} arma_rnd (@var{a}, @var{b}, @var{v}, @var{t}, @var{n}) |
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22 ## Return a simulation of the ARMA model |
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23 ## |
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24 ## @example |
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25 ## x(n) = a(1) * x(n-1) + ... + a(k) * x(n-k) |
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26 ## + e(n) + b(1) * e(n-1) + ... + b(l) * e(n-l) |
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27 ## @end example |
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28 ## |
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29 ## @noindent |
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30 ## in which @var{k} is the length of vector @var{a}, @var{l} is the |
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31 ## length of vector @var{b} and @var{e} is gaussian white noise with |
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32 ## variance @var{v}. The function returns a vector of length @var{t}. |
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33 ## |
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34 ## The optional parameter @var{n} gives the number of dummy |
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35 ## @var{x}(@var{i}) used for initialization, i.e., a sequence of length |
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36 ## @var{t}+@var{n} is generated and @var{x}(@var{n}+1:@var{t}+@var{n}) |
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37 ## is returned. If @var{n} is omitted, @var{n} = 100 is used. |
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38 ## @end deftypefn |
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39 |
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40 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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41 ## Description: Simulate an ARMA process |
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42 |
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43 function x = arma_rnd (a, b, v, t, n) |
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44 |
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45 if (nargin == 4) |
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46 n = 100; |
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47 elseif (nargin == 5) |
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48 if (!isscalar (t)) |
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49 error ("arma_rnd: n must be a scalar"); |
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50 endif |
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51 else |
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52 print_usage (); |
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53 endif |
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54 |
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55 if ((min (size (a)) > 1) || (min (size (b)) > 1)) |
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56 error ("arma_rnd: a and b must not be matrices"); |
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57 endif |
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58 |
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59 if (!isscalar (t)) |
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60 error ("arma_rnd: t must be a scalar"); |
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61 endif |
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62 |
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63 ar = length (a); |
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64 br = length (b); |
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65 |
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66 a = reshape (a, ar, 1); |
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67 b = reshape (b, br, 1); |
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68 |
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69 a = [1; -a]; # apply our notational convention |
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70 b = [1; b]; |
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71 |
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72 n = min (n, ar + br); |
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73 |
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74 e = sqrt (v) * randn (t + n, 1); |
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75 |
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76 x = filter (b, a, e); |
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77 x = x(n + 1 : t + n); |
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78 |
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79 endfunction |
