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vol.m

## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007
##               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 3 of the License, 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 program; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} vol (@var{x}, @var{m}, @var{n})
## Return the volatility of each column of the input matrix @var{x}.
## The number of data sets per period is given by @var{m} (e.g. the
## number of data per year if you want to compute the volatility per
## year).  The optional parameter @var{n} gives the number of past
## periods used for computation, if it is omitted, a value of 1 is used.
## If @var{t} is the number of rows of @var{x}, @code{vol} returns the
## volatility from @code{n*m} to @var{t}.
## @end deftypefn

## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description: Volatility of financial time series data

function retval = vol (X, m, n)

  if (nargin < 2)
    print_usage ();
  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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