maint: Use Octave coding conventions for cuddling parentheses in scripts directory * lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m, colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m, int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m, __isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m, rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m, inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m, gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m, ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m, compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m, getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m, __xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m, fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m, copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m, installed_packages.m, is_architecture_dependent.m, load_package_dirs.m, print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m, allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m, comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m, fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m, polar.m, print.m, __add_datasource__.m, __add_default_menu__.m, __axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m, __errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m, __ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m, __go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m, __stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m, surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m, mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m, addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m, arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m, hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m, stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m, __sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m, magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m, quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m, bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m, kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m, z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m, strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m, test.m, now.m: Use Octave coding conventions for cuddling parentheses in scripts directory.

## Copyright (C) 1995-2012 Kurt Hornik
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} arch_rnd (@var{a}, @var{b}, @var{t})
## Simulate an ARCH sequence of length @var{t} with AR
## coefficients @var{b} and CH coefficients @var{a}.  I.e., the result
## @math{y(t)} follows the model
## @c Set example in small font to prevent overfull line
##
## @smallexample
## y(t) = b(1) + b(2) * y(t-1) + @dots{} + b(lb) * y(t-lb+1) + e(t),
## @end smallexample
##
## @noindent
## where @math{e(t)}, given @var{y} up to time @math{t-1}, is
## @math{N(0, h(t))}, with
## @c Set example in small font to prevent overfull line
##
## @smallexample
## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(la) * e(t-la+1)^2
## @end smallexample
## @end deftypefn

## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Simulate an ARCH process

function y = arch_rnd (a, b, t)

  if (nargin != 3)
    print_usage ();
  endif

  if (! ((min (size (a)) == 1) && (min (size (b)) == 1)))
    error ("arch_rnd: A and B must both be scalars or vectors");
  endif
  if (! (isscalar (t) && (t > 0) && (rem (t, 1) == 0)))
    error ("arch_rnd: T must be a positive integer");
  endif

  if (! (a(1) > 0))
    error ("arch_rnd: A(1) must be positive");
  endif
  ## perhaps add a test for the roots of a(z) here ...

  la = length (a);
  a  = reshape (a, 1, la);
  if (la == 1)
    a  = [a, 0];
    la = la + 1;
  endif

  lb = length (b);
  b  = reshape (b, 1, lb);
  if (lb == 1)
    b  = [b, 0];
    lb = lb + 1;
  endif
  m  = max ([la, lb]);

  e  = zeros (t, 1);
  h  = zeros (t, 1);
  y  = zeros (t, 1);

  h(1) = a(1);
  e(1) = sqrt (h(1)) * randn;
  y(1) = b(1) + e(1);

  for t = 2:m
    ta   = min ([t, la]);
    h(t) = a(1) + a(2:ta) * e(t-ta+1:t-1).^2;
    e(t) = sqrt (h(t)) * randn;
    tb   = min ([t, lb]);
    y(t) = b(1) + b(2:tb) * y(t-tb+1:t-1) + e(t);
  endfor

  if (t > m)
    for t = m+1:t
      h(t) = a(1) + a(2:la) * e(t-la+1:t-1).^2;
      e(t) = sqrt (h(t)) * randn;
      y(t) = b(1) + b(2:lb) * y(t-tb+1:t-1) + e(t);
    endfor
  endif

  y = y(1:t);

endfunction