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## Copyright (C) 1995, 1996, 1997 Friedrich Leisch
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: vol (X, m [, n])
##
## vol returns the volatility of each column of the input matrix X. m is
## the number of data sets per period (e.g. the number of data per year
## if you want to compute the volatility per year). The optional
## parameter n gives the number of past periods used for computation, if
## n is omitted, n=1 is used. If T is the number of rows of X, vol
## returns the volatility from n*m to T.
## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description: Volatility of financial time series data
function retval = vol (X, m, n)
if (nargin < 2)
usage ("vol (X, m [, n])");
endif
[xr, xc] = size (X);
if (nargin > 2)
if (n * m > xr)
error ("vol: I need more data!");
endif
else
n = 1;
if (n * m > xr)
error ("vol: I need more data!");
endif
endif
U = zeros (xr - 1, xc);
if all (X)
U = X ((2 : xr), :) ./ X((1 : (xr-1)), :);
else
error ("vol: zero element in X");
endif
U = log(U);
U = U - ones (xr - 1, 1) * sum (U) / (xr - 1);
retval = zeros (xr - n * m, xc);
retval(1, :) = sumsq (U((1 : n*m), :));
for i = 2 : (xr - n * m)
retval(i, :) = retval(i - 1, :) ...
- U(i - 1, :).^2 + U(i + n * m - 1, :).^2;
endfor
retval = sqrt (retval * m / (n * m - 1));
endfunction
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