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comparison scripts/signal/arch_fit.m @ 20200:f1d0f506ee78 stable

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doc: Update more docstrings to have one sentence summary as first line. Reviewed optimization, polynomial, signal script directories. * scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/lsqnonneg.m, scripts/optimization/pqpnonneg.m, scripts/optimization/qp.m, scripts/optimization/sqp.m, scripts/polynomial/compan.m, scripts/polynomial/mkpp.m, scripts/polynomial/mpoles.m, scripts/polynomial/pchip.m, scripts/polynomial/poly.m, scripts/polynomial/polyaffine.m, scripts/polynomial/polyder.m, scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m, scripts/polynomial/polygcd.m, scripts/polynomial/polyint.m, scripts/polynomial/polyout.m, scripts/polynomial/polyval.m, scripts/polynomial/ppder.m, scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m, scripts/polynomial/ppval.m, scripts/polynomial/residue.m, scripts/polynomial/roots.m, scripts/polynomial/spline.m, scripts/polynomial/splinefit.m, scripts/polynomial/unmkpp.m, scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m, scripts/signal/arma_rnd.m, scripts/signal/autoreg_matrix.m, scripts/signal/bartlett.m, scripts/signal/blackman.m, scripts/signal/detrend.m, scripts/signal/diffpara.m, scripts/signal/durbinlevinson.m, scripts/signal/fftconv.m, scripts/signal/fftfilt.m, scripts/signal/fftshift.m, scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/hamming.m, scripts/signal/hanning.m, scripts/signal/hurst.m, scripts/signal/ifftshift.m, scripts/signal/periodogram.m, scripts/signal/sinc.m, scripts/signal/sinetone.m, scripts/signal/sinewave.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/signal/spencer.m, scripts/signal/stft.m, scripts/signal/synthesis.m, scripts/signal/unwrap.m, scripts/signal/yulewalker.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Mon, 04 May 2015 21:50:57 -0700
parents 9fc020886ae9
children 83792dd9bcc1
comparison
equal deleted inserted replaced
20199:df437a52bcaf 20200:f1d0f506ee78
16 ## along with Octave; see the file COPYING. If not, see 16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>. 17 ## <http://www.gnu.org/licenses/>.
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {[@var{a}, @var{b}] =} arch_fit (@var{y}, @var{x}, @var{p}, @var{iter}, @var{gamma}, @var{a0}, @var{b0}) 20 ## @deftypefn {Function File} {[@var{a}, @var{b}] =} arch_fit (@var{y}, @var{x}, @var{p}, @var{iter}, @var{gamma}, @var{a0}, @var{b0})
21 ## Fit an ARCH regression model to the time series @var{y} using the 21 ## Fit an ARCH regression model to the time series @var{y} using the scoring
22 ## scoring algorithm in @nospell{Engle's} original ARCH paper. The model is 22 ## algorithm in @nospell{Engle's} original ARCH paper.
23 ##
24 ## The model is
23 ## 25 ##
24 ## @example 26 ## @example
25 ## @group 27 ## @group
26 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t), 28 ## y(t) = b(1) * x(t,1) + @dots{} + b(k) * x(t,k) + e(t),
27 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(p+1) * e(t-p)^2 29 ## h(t) = a(1) + a(2) * e(t-1)^2 + @dots{} + a(p+1) * e(t-p)^2
28 ## @end group 30 ## @end group
29 ## @end example 31 ## @end example
30 ## 32 ##
31 ## @noindent 33 ## @noindent
32 ## in which @math{e(t)} is @math{N(0, h(t))}, given a time-series vector 34 ## in which @math{e(t)} is @math{N(0, h(t))}, given a time-series vector
33 ## @var{y} up to time @math{t-1} and a matrix of (ordinary) regressors 35 ## @var{y} up to time @math{t-1} and a matrix of (ordinary) regressors @var{x}
34 ## @var{x} up to @math{t}. The order of the regression of the residual 36 ## up to @math{t}. The order of the regression of the residual variance is
35 ## variance is specified by @var{p}. 37 ## specified by @var{p}.
36 ## 38 ##
37 ## If invoked as @code{arch_fit (@var{y}, @var{k}, @var{p})} with a 39 ## If invoked as @code{arch_fit (@var{y}, @var{k}, @var{p})} with a positive
38 ## positive integer @var{k}, fit an ARCH(@var{k}, @var{p}) process, 40 ## integer @var{k}, fit an ARCH(@var{k}, @var{p}) process, i.e., do the above
39 ## i.e., do the above with the @math{t}-th row of @var{x} given by 41 ## with the @math{t}-th row of @var{x} given by
40 ## 42 ##
41 ## @example 43 ## @example
42 ## [1, y(t-1), @dots{}, y(t-k)] 44 ## [1, y(t-1), @dots{}, y(t-k)]
43 ## @end example 45 ## @end example
44 ## 46 ##
45 ## Optionally, one can specify the number of iterations @var{iter}, the 47 ## Optionally, one can specify the number of iterations @var{iter}, the
46 ## updating factor @var{gamma}, and initial values @math{a0} and 48 ## updating factor @var{gamma}, and initial values @math{a0} and @math{b0}
47 ## @math{b0} for the scoring algorithm. 49 ## for the scoring algorithm.
48 ## @end deftypefn 50 ## @end deftypefn
49 51
50 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> 52 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
51 ## Description: Fit an ARCH regression model 53 ## Description: Fit an ARCH regression model
52 54