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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 ## usage: [d, D] = diffpara (X [, a [, b]]) |
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18 ## |
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19 ## Returns the estimator 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 [2*pi*a/T, 2*pi*b/T] are used for the |
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23 ## estimation. If b is omitted, the interval [2*pi/T, 2*pi*a/T] is used, |
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24 ## if both b and a are omitted then a = 0.5 * sqrt(T) and b = 1.5 * |
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25 ## sqrt(T) is used, where T is the sample size. If X is a matrix, the |
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26 ## differencing parameter of every single column is estimated. |
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27 ## |
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28 ## D contains the estimators for all frequencies in the intervals |
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29 ## described above, d is simply mean(D). |
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30 ## |
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31 ## Reference: Brockwell, Peter J. & Davis, Richard A. Time Series: |
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32 ## Theory and Methods Springer 1987 |
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33 |
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34 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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35 ## Description: Estimate the fractional differencing parameter |
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36 |
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37 function [d, D] = diffpara (X, a, b) |
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38 |
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39 if ((nargin < 1) || (nargin > 3)) |
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40 usage ("[d [, D]] = diffpara (X [, a [, b]])"); |
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41 else |
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42 if is_vector (X) |
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43 n = length (X); |
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44 k = 1; |
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45 X = reshape (X, n, 1); |
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46 else |
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47 [n, k] = size(X); |
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48 endif |
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49 if (nargin == 1) |
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50 a = 0.5 * sqrt (n); |
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51 b = 1.5 * sqrt (n); |
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52 elseif (nargin == 2) |
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53 b = a; |
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54 a = 1; |
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55 endif |
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56 endif |
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57 |
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58 if !(is_scalar (a) && is_scalar (b)) |
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59 error ("diffpara: a and b must be scalars"); |
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60 endif |
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61 |
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62 D = zeros (b - a + 1, k); |
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63 |
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64 for l = 1:k |
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65 |
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66 w = 2 * pi * (1 : n-1) / n; |
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67 |
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68 x = 2 * log (abs( 1 - exp (-i*w))); |
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69 y = log (periodogram (X(2:n,l))); |
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70 |
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71 x = center (x); |
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72 y = center (y); |
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73 |
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74 for m = a:b |
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75 D(m-a+1) = - x(1:m) * y(1:m) / sumsq (x(1:m)); |
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76 endfor |
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77 |
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78 endfor |
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79 |
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80 d = mean (D); |
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81 |
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82 endfunction |
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83 |
