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garch

garch estimation

CALLING SEQUENCE

[rgarch]=garch(namey,arg1,...,argn)

PARAMETERS

Input

* namey = a time series, a real (nx1) vector or a string equal to the name of a time series or a (nx1) real vector between quotes

* argi = an argument which can be:

  - a time series

  - a real (nxp) vector

  -  a string equal to the name of a time series or a (nxp) real vector between quotes

  - the string 'noprint' if the user doesn't want to print the results of the regression

  - 'b = xx' where xx is a (k x 1) vector of B starting values

  - 'b = xx' where xx is a (k x 1) vector of B starting values

  - 'a0 = xx' where xx is a0 starting values to feed the maximisation programm

  - 'ar = xx' where xx is (p x 1) vector of ar starting values to feed the maximisation programm

  - 'ma = xx' where xx is (q x 1) vector of ma starting values to feed the maximisation programm

  - 'meth=maxlik' or 'meth=optim' (default)

  - any option to maxlik (see maxlik for a list)

  - the string 'dropna' if the user wants to remove the NA values from the data

  -  'optfunc=optim' if the user wants to use the optim optimisation function (default: optimg)

  -  'opt_nelmead=crit,nitermax' with crit the value of the convergence criterion in the Nelder-Meade optimisation function and nitermax the maximum number of iterations (default = 'opt_nelmead=2*%eps,1000')

  -  'opt_optim=opts' where opts are options for optim that can be entered after the starting value of the parameters (default = 'opt_optim=,''ar'',1e6,1e6'')

  -  'opt_convg=val' where val is the threshold on gradient norm (default = 'opt_convg=1e-5')

 

Output

* rgarcha result tlist with:

  - rgarch('meth') = 'garch'

  - rgarch('optmeth') = 'optim' or 'maxlik' (method used (the optimisation)

  - rgarch('y') = y data vector

  - rgarch('x') = x data matrix

  - rgarch('nobs') = # observations

  - rgarch('nvar') = # variables

  - rgarch('beta') = bhat

  - rgarch('yhat') = yhat

  - rgarch('resid') = residuals

  - rgarch('vcovar') = estimated variance-covariance matrix of beta

  - rgarch('sige') = estimated variance of the residuals

  - rgarch('sigu') = sum of squared residuals

  - rgarch('ser') = standard error of the regression

  - rgarch('tstat') = t-stats

  - rgarch('pvalue') = pvalue of the betas

  - rgarch('dw') = Durbin-Watson Statistic

  - rgarch('condindex') = multicolinearity cond index

  - rgarch('prescte') = boolean indicating the presence or absence of a constant in the regression

  - rgarch('b') = estimated b

  - rgarch('a0') = estimated a0

  - rgarch('ar') = estimated ar

  - rgarch('ma') = estimated ma

  - rgarch('sigt') = estimated h(t)

  - rgarch('like') = log-likelihood

  - rgarch('parm1') = vector of stacked parameters

  - rgarch('aic') = Akaïke information criterion

  - rgarch('bic') = Schwarz information criterion

  - rgarch('hq') = Hannan-Quinn information criterion

  - rgarch('rbar') = rbar-squared

  - rgarch('f') = F-stat for the nullity of coefficients other than the constant

  - rgarch('pvaluef') = its significance level

  - rgarch('prests') = boolean indicating the presence or absence of a time series in the regression

  - rgarch('namey') = name of the y variable

  - rgarch('namex') = name of the x variables

  - rgarch('dropna') = boolean indicating if NAs have been dropped

  - rgarch('bounds') = if there is a timeseries in the forecast, the bounds of the regression

  - rgarch('nonna') = vector indicating position of non-NAs

DESCRIPTION

Estimates a regression with garch(p,q) errors:

y(t) = X(t)*b + e(t), e(t) = N(0,h(t))

h(t) = a0 +

ar(1)*h(t-1) + ... + ar(p)*h(t-p) + ma(1)*e(t-1)^2 + ... + ma(q)*e(t-q)^2

EXAMPLE

load(GROCERDIR+'/data/garchd.dat')
 
bounds('1949q1','1983q4')
r1 = ols('gnpdef','cte','lagts(gnpdef)','lagts(2,gnpdef)','lagts(3,gnpdef)','lagts(4,gnpdef)');
bet = r1('beta');
s = r1('ser');
 
r2 = garch('gnpdef','cte','lagts(gnpdef)','lagts(2,gnpdef)','lagts(3,gnpdef)','lagts(4,gnpdef)','a0=s','ar=0','ma=0','b=bet');
 
// Example taken from function garch_d(). Estimates a garch(1,1) model, taken from Greene's book. Starting values for a0, ar and ma are
// s (in garch_d, s is the estimated variance of the corresponding ols model), 0 and 0. Starting value for b is also taken from
// ols estimation. Optimisation method is maxlik.

AUTHOR

Eric Dubois 2002-2007

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