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1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 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} {[@var{d}, @var{dd}] =} diffpara (@var{x}, @var{a}, @var{b}) |
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22 ## Return the estimator @var{d} for the differencing parameter of an |
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23 ## integrated time series. |
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24 ## |
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25 ## The frequencies from @math{[2*pi*a/t, 2*pi*b/T]} are used for the |
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26 ## estimation. If @var{b} is omitted, the interval |
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27 ## @math{[2*pi/T, 2*pi*a/T]} is used. If both @var{b} and @var{a} are |
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28 ## omitted then @math{a = 0.5 * sqrt (T)} and @math{b = 1.5 * sqrt (T)} |
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29 ## is used, where @math{T} is the sample size. If @var{x} is a matrix, |
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30 ## the differencing parameter of each column is estimated. |
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31 ## |
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32 ## The estimators for all frequencies in the intervals |
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33 ## described above is returned in @var{dd}. The value of @var{d} is |
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34 ## simply the mean of @var{dd}. |
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35 ## |
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36 ## Reference: Brockwell, Peter J. & Davis, Richard A. Time Series: |
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37 ## Theory and Methods Springer 1987. |
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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: Estimate the fractional differencing parameter |
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42 |
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43 function [d, D] = diffpara (X, a, b) |
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44 |
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45 if ((nargin < 1) || (nargin > 3)) |
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46 print_usage (); |
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47 else |
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48 if (isvector (X)) |
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49 n = length (X); |
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50 k = 1; |
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51 X = reshape (X, n, 1); |
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52 else |
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53 [n, k] = size(X); |
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54 endif |
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55 if (nargin == 1) |
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56 a = 0.5 * sqrt (n); |
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57 b = 1.5 * sqrt (n); |
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58 elseif (nargin == 2) |
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59 b = a; |
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60 a = 1; |
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61 endif |
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62 endif |
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63 |
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64 if (! (isscalar (a) && isscalar (b))) |
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65 error ("diffpara: a and b must be scalars"); |
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66 endif |
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67 |
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68 D = zeros (b - a + 1, k); |
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69 |
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70 for l = 1:k |
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71 |
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72 w = 2 * pi * (1 : n-1) / n; |
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73 |
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74 x = 2 * log (abs (1 - exp (-i*w))); |
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75 y = log (periodogram (X(2:n,l))); |
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76 |
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77 x = center (x); |
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78 y = center (y); |
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79 |
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80 for m = a:b |
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81 D(m-a+1) = - x(1:m) * y(1:m) / sumsq (x(1:m)); |
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82 endfor |
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83 |
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84 endfor |
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85 |
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86 d = mean (D); |
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87 |
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88 endfunction |
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89 |
