Mercurial > hg > octave-nkf
annotate scripts/signal/diffpara.m @ 20802:5fc798a9b32c
maint: Periodic merge of stable to default.
| author | Rik <rik@octave.org> |
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| date | Fri, 09 Oct 2015 19:28:05 -0700 |
| parents | f1d0f506ee78 |
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| rev | line source |
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1 ## Copyright (C) 1995-2015 Friedrich Leisch |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3191 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3191 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3191 | 18 |
| 3449 | 19 ## -*- texinfo -*- |
| 6547 | 20 ## @deftypefn {Function File} {[@var{d}, @var{dd}] =} diffpara (@var{x}, @var{a}, @var{b}) |
| 3449 | 21 ## Return the estimator @var{d} for the differencing parameter of an |
| 3191 | 22 ## integrated time series. |
| 23 ## | |
| 3499 | 24 ## The frequencies from @math{[2*pi*a/t, 2*pi*b/T]} are used for the |
| 25 ## estimation. If @var{b} is omitted, the interval | |
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26 ## @math{[2*pi/T, 2*pi*a/T]} is used. If both @var{b} and @var{a} are omitted |
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27 ## then @math{a = 0.5 * sqrt (T)} and @math{b = 1.5 * sqrt (T)} is used, where |
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28 ## @math{T} is the sample size. If @var{x} is a matrix, the differencing |
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29 ## parameter of each column is estimated. |
| 3191 | 30 ## |
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31 ## The estimators for all frequencies in the intervals described above is |
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32 ## returned in @var{dd}. |
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33 ## |
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34 ## The value of @var{d} is simply the mean of @var{dd}. |
| 3191 | 35 ## |
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36 ## Reference: @nospell{P.J. Brockwell & R.A. Davis}. @cite{Time Series: |
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37 ## Theory and Methods}. Springer 1987. |
| 3449 | 38 ## @end deftypefn |
| 3426 | 39 |
| 3457 | 40 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
| 41 ## Description: Estimate the fractional differencing parameter | |
| 3191 | 42 |
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43 function [d, dd] = diffpara (x, a, b) |
| 3426 | 44 |
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45 if (nargin < 1 || nargin > 3) |
| 6046 | 46 print_usage (); |
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47 endif |
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48 |
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49 if (isvector (x)) |
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50 n = length (x); |
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51 k = 1; |
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52 x = reshape (x, n, 1); |
| 3191 | 53 else |
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54 [n, k] = size (x); |
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55 endif |
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56 if (nargin == 1) |
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57 a = 0.5 * sqrt (n); |
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58 b = 1.5 * sqrt (n); |
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59 elseif (nargin == 2) |
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60 b = a; |
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61 a = 1; |
| 3191 | 62 endif |
| 3426 | 63 |
| 4030 | 64 if (! (isscalar (a) && isscalar (b))) |
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65 error ("diffpara: A and B must be scalars"); |
| 3191 | 66 endif |
| 3426 | 67 |
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68 dd = zeros (b - a + 1, k); |
| 3426 | 69 |
| 3191 | 70 for l = 1:k |
| 3426 | 71 |
| 3191 | 72 w = 2 * pi * (1 : n-1) / n; |
| 3426 | 73 |
| 3457 | 74 x = 2 * log (abs (1 - exp (-i*w))); |
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75 y = log (periodogram (x(2:n,l))); |
| 3426 | 76 |
| 3191 | 77 x = center (x); |
| 78 y = center (y); | |
| 3426 | 79 |
| 3191 | 80 for m = a:b |
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81 dd(m-a+1) = - x(1:m) * y(1:m) / sumsq (x(1:m)); |
| 3191 | 82 endfor |
| 3426 | 83 |
| 3191 | 84 endfor |
| 3426 | 85 |
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86 d = mean (dd); |
| 3426 | 87 |
| 3191 | 88 endfunction |
| 89 |