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1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2006, |
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2 ## 2007 Kurt Hornik |
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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} {} arch_rnd (@var{a}, @var{b}, @var{t}) |
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22 ## Simulate an ARCH sequence of length @var{t} with AR |
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23 ## coefficients @var{b} and CH coefficients @var{a}. I.e., the result |
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24 ## @math{y(t)} follows the model |
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25 ## |
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26 ## @smallexample |
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27 ## y(t) = b(1) + b(2) * y(t-1) + @dots{} + b(lb) * y(t-lb+1) + e(t), |
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28 ## @end smallexample |
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29 ## |
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30 ## @noindent |
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31 ## where @math{e(t)}, given @var{y} up to time @math{t-1}, is |
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32 ## @math{N(0, h(t))}, with |
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33 ## |
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34 ## @smallexample |
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35 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(la) * e(t-la+1)^2 |
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36 ## @end smallexample |
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37 ## @end deftypefn |
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38 |
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39 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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40 ## Description: Simulate an ARCH process |
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41 |
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42 function y = arch_rnd (a, b, T) |
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43 |
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44 if (nargin != 3) |
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45 print_usage (); |
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46 endif |
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47 |
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48 if (! ((min (size (a)) == 1) && (min (size (b)) == 1))) |
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49 error ("arch_rnd: a and b must both be scalars or vectors"); |
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50 endif |
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51 if (! (isscalar (T) && (T > 0) && (rem (T, 1) == 0))) |
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52 error ("arch_rnd: T must be a positive integer"); |
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53 endif |
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54 |
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55 if (! (a(1) > 0)) |
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56 error ("arch_rnd: a(1) must be positive"); |
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57 endif |
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58 ## perhaps add a test for the roots of a(z) here ... |
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59 |
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60 la = length (a); |
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61 a = reshape (a, 1, la); |
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62 if (la == 1) |
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63 a = [a, 0]; |
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64 la = la + 1; |
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65 endif |
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66 |
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67 lb = length (b); |
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68 b = reshape (b, 1, lb); |
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69 if (lb == 1) |
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70 b = [b, 0]; |
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71 lb = lb + 1; |
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72 endif |
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73 M = max([la, lb]); |
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74 |
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75 e = zeros (T, 1); |
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76 h = zeros (T, 1); |
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77 y = zeros (T, 1); |
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78 |
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79 h(1) = a(1); |
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80 e(1) = sqrt (h(1)) * randn; |
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81 y(1) = b(1) + e(1); |
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82 |
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83 for t = 2:M |
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84 ta = min ([t, la]); |
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85 h(t) = a(1) + a(2:ta) * e(t-ta+1:t-1).^2; |
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86 e(t) = sqrt (h(t)) * randn; |
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87 tb = min ([t, lb]); |
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88 y(t) = b(1) + b(2:tb) * y(t-tb+1:t-1) + e(t); |
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89 endfor |
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90 |
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91 if (T > M) |
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92 for t = M+1:T |
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93 h(t) = a(1) + a(2:la) * e(t-la+1:t-1).^2; |
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94 e(t) = sqrt (h(t)) * randn; |
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95 y(t) = b(1) + b(2:lb) * y(t-tb+1:t-1) + e(t); |
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96 endfor |
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97 endif |
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98 |
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99 y = y(1:T); |
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100 |
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101 endfunction |
