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1 ## Copyright (C) 1995, 1996, 1997 Friedrich Leisch |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{d}, @var{D}]} = diffpara (@var{x}, @var{a}, @var{b}) |
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19 ## Return the estimator @var{d} for the differencing parameter of an |
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20 ## integrated time series. |
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21 ## |
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22 ## The frequencies from @code{[2*pi*@var{a}/@var{T}, |
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23 ## 2*pi*@var{b}/@var{T}]} are used for the estimation. If @var{b} is |
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24 ## omitted, the interval @code{[2*pi/@var{T}, 2*pi*@var{a}/@var{T}]} is |
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25 ## used. If both @var{b} and @var{a} are omitted then @code{@var{a} = |
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26 ## 0.5 * sqrt(@var{T})} and @code{@var{b} = 1.5 * sqrt(@var{T})} is |
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27 ## used, where @var{T} is the sample size. If @var{x} is a matrix, the |
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28 ## differencing parameter of each column is estimated. |
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29 ## |
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30 ## The estimators for all frequencies in the intervals |
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31 ## described above is returned in @var{D}. The value of @var{d} is |
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32 ## simply the mean of @var{D}. |
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33 ## |
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34 ## Reference: Brockwell, Peter J. & Davis, Richard A. Time Series: |
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35 ## Theory and Methods Springer 1987. |
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36 ## @end deftypefn |
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37 |
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38 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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39 ## Description: Estimate the fractional differencing parameter |
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40 |
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41 function [d, D] = diffpara (X, a, b) |
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42 |
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43 if ((nargin < 1) || (nargin > 3)) |
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44 usage ("[d, D] = diffpara (X, a, b)"); |
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45 else |
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46 if (is_vector (X)) |
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47 n = length (X); |
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48 k = 1; |
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49 X = reshape (X, n, 1); |
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50 else |
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51 [n, k] = size(X); |
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52 endif |
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53 if (nargin == 1) |
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54 a = 0.5 * sqrt (n); |
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55 b = 1.5 * sqrt (n); |
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56 elseif (nargin == 2) |
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57 b = a; |
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58 a = 1; |
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59 endif |
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60 endif |
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61 |
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62 if (! (is_scalar (a) && is_scalar (b))) |
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63 error ("diffpara: a and b must be scalars"); |
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64 endif |
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65 |
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66 D = zeros (b - a + 1, k); |
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67 |
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68 for l = 1:k |
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69 |
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70 w = 2 * pi * (1 : n-1) / n; |
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71 |
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72 x = 2 * log (abs (1 - exp (-i*w))); |
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73 y = log (periodogram (X(2:n,l))); |
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74 |
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75 x = center (x); |
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76 y = center (y); |
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77 |
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78 for m = a:b |
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79 D(m-a+1) = - x(1:m) * y(1:m) / sumsq (x(1:m)); |
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80 endfor |
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81 |
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82 endfor |
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83 |
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84 d = mean (D); |
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85 |
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86 endfunction |
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87 |
