ugarchfit-methods {rugarch}

function: Univariate GARCH Fitting

Description

Method for fitting a variety of univariate GARCH models.

Usage

ugarchfit(spec, data, out.sample = 0, solver = "solnp", solver.control = list(),
fit.control = list(stationarity = 1, fixed.se = 0, scale = 0, rec.init = 'all',
trunclag = 1000),
numderiv.control = list(grad.eps=1e-4, grad.d=0.0001,
grad.zero.tol=sqrt(.Machine$double.eps/7e-7), hess.eps=1e-4, hess.d=0.1,
hess.zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2),...)

Arguments

data

A univariate data object. Can be a numeric vector, matrix, data.frame, zoo, xts, timeSeries, ts or irts object.

spec

A univariate GARCH spec object of class uGARCHspec.

out.sample

A positive integer indicating the number of periods before the last to keep for out of sample forecasting (see details).

solver

One of either “nlminb”, “solnp”, “lbfgs”, “gosolnp”, “nloptr” or “hybrid” (see notes).

solver.control

Control arguments list passed to optimizer.

fit.control

Control arguments passed to the fitting routine. Stationarity explicitly imposes the variance stationarity constraint during optimization. For the FIGARCH model this imposes the positivity constraint. The fixed.se argument controls whether standard errors should be calculated for those parameters which were fixed (through the fixed.pars argument of the ugarchspec function). The scale parameter controls whether the data should be scaled before being submitted to the optimizer. The rec.init option determines the type of initialization for the variance recursion. Valid options are ‘all’ which uses all the values for the unconditional variance calculation, an integer greater than or equal to 1 denoting the number of data points to use for the calculation, or a positive numeric value less than one which determines the weighting for use in an exponential smoothing backcast. The trunclag is the truncation lags for the binomial expansion in the FIGARCH model.

numderiv.control

Control arguments passed to the numerical routines for the calculation of the standard errors. See the documentation in the numDeriv package for further details. The arguments which start with ‘hess’ are passed to the hessian routine while those with ‘grad’ to the jacobian routine.

...

For the multiplicative component sGARCH model (mcsGARCH), the additional argument ‘DailyVar’ is required and should be an xts object of the daily forecasted variance to use with the intraday data.

Details

The GARCH optimization routine first calculates a set of feasible starting points which are used to initiate the GARCH recursion. The main part of the likelihood calculation is performed in C-code for speed.
The out.sample option is provided in order to carry out forecast performance testing against actual data. A minimum of 5 data points are required for these tests. If the out.sample option is positive, then the routine will fit only N - out.sample (where N is the total data length) data points, leaving out.sample points for forecasting and testing using the forecast performance measures. In the ugarchforecast routine the n.ahead may also be greater than the out.sample number resulting in a combination of out of sample data points matched against actual data and some without, which the forecast performance tests will ignore.
The “gosolnp” solver allows for the initialization of multiple restarts of the solnp solver with randomly generated parameters (see documentation in the Rsolnp-package for details of the strategy used). The solver.control list then accepts the following additional (to the solnp) arguments: “n.restarts” is the number of solver restarts required (defaults to 1), “parallel” (logical), “pkg” (either snowfall or multicore) and “cores” (the number of cores or workers to use) for use of parallel functionality, “rseed” is the seed to initialize the random number generator, and “n.sim” is the number of simulated parameter vectors to generate per n.restarts.
The “hybrid” strategy solver first tries the “solnp” solver, in failing to converge then tries then “nlminb”, the “gosolnp” and finally the “nloptr” solvers. Solver control parameters can be passed for all the solvers in the solver.control list as one long list which will be filtered for each solver's specific options as and when that solver is called during the hybrid strategy optimization. It is still possible that the Hessian at the optimal found cannot be inverted, in which case a warning is printed and there will not be any standard errors. In this case it is suggested that the problem is re-run with different solver parameters. It is also possible that the solution, while still ‘almost’ optimal may be at a saddle-point very near the global optimum in which case the Hessian may still be invertible but one eigenvalue is negative. The uGARCHfit object has a value in the fit slot called condH (object@fit$condH) which indicates the approximate number of decimal places lost to roundoff/numerical estimation error. When this is NaN, this indicates the case just described of one negative eigenvalue/saddlepoint (this previously flagged a warning but is now silenced and it is upto to the user to decide whether it is worth investigating further).

Value

A uGARCHfit object containing details of the GARCH fit.

Note

The nloptr solver takes the following options in the solver.control list:

	ftol_rel	function value relative tolerance	default: 1e-8
	xtol_rel	parameter value relative tolerance	default: 1e-6
	maxeval	maximum function evaluations	default: 25000
	print_level	trace level	default: 1
	solver	the nloptr solver to use	default: 1 (‘SBPLX’).

The solver option for nloptr has 10 different choices (1:10), which are 1:‘COBYLA’, 2:‘BOBYQA’, 3:‘PRAXIS’, 4:‘NELDERMEAD’, 5:‘SBPLX’, 6:‘AUGLAG’+‘COBYLA’, 7:‘AUGLAG’+‘BOBYQA’, 8:‘AUGLAG’+‘PRAXIS’, 9:‘AUGLAG’+‘NELDERMEAD’ and 10:‘AUGLAG’+‘SBPLX’. As always, your mileage will vary and care should be taken on the choice of solver, tuning parameters etc. If you do use this solver try 9 or 10 first.

Author(s)

Alexios Ghalanos

See Also

For specification ugarchspec,filtering ugarchfilter, forecasting ugarchforecast, simulation ugarchsim, rolling forecast and estimation ugarchroll, parameter distribution and uncertainty ugarchdistribution, bootstrap forecast ugarchboot.

Examples

# Basic GARCH(1,1) Spec
data(dmbp)
spec = ugarchspec()
fit = ugarchfit(data = dmbp[,1], spec = spec)
fit
coef(fit)
head(sigma(fit))
#plot(fit,which="all")
# in order to use fpm (forecast performance measure function)
# you need to select a subsample of the data:
spec = ugarchspec()
fit = ugarchfit(data = dmbp[,1], spec = spec, out.sample=100)
forc = ugarchforecast(fit, n.ahead=100)
# this means that 100 data points are left from the end with which to
# make inference on the forecasts
fpm(forc)