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binoinv.m: Implement binary search algorithm for 28X performance increase (bug #34363). * binoinv.m: Call new functions scalar_binoinv or vector_binoinv to calculate binoinv. If there are still uncalculated values then call bin_search_binoinv to perform binary search for remaining values. Add more BIST tests. * binoinv.m (scalar_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000. * binoinv.m (vector_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000.
author Lachlan Andrew <lachlanbis@gmail.com>
date Sun, 11 Oct 2015 19:49:40 -0700
parents f1d0f506ee78
children
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1 ## Copyright (C) 1995-2015 Friedrich Leisch
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{d}, @var{dd}] =} diffpara (@var{x}, @var{a}, @var{b})
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21 ## Return the estimator @var{d} for the differencing parameter of an
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22 ## integrated time series.
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23 ##
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24 ## The frequencies from @math{[2*pi*a/t, 2*pi*b/T]} are used for the
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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.
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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}.
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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.
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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, dd] = 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 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);
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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;
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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 dd = 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 dd(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 (dd);
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87
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88 endfunction
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89