garchFitControl function

Control GARCH fitting algorithms

Control parameters for the GARCH fitting algorithms.

garchFitControl(
    llh = c("filter", "internal", "testing"),
    nlminb.eval.max = 2000,
    nlminb.iter.max = 1500,
    nlminb.abs.tol = 1.0e-20,
    nlminb.rel.tol = 1.0e-14,
    nlminb.x.tol = 1.0e-14,
    nlminb.step.min = 2.2e-14,
    nlminb.scale = 1,
    nlminb.fscale = FALSE,
    nlminb.xscale = FALSE,
    sqp.mit = 200,
    sqp.mfv = 500,
    sqp.met = 2,
    sqp.mec = 2,
    sqp.mer = 1,
    sqp.mes = 4,
    sqp.xmax = 1.0e3,
    sqp.tolx = 1.0e-16,
    sqp.tolc = 1.0e-6,
    sqp.tolg = 1.0e-6,
    sqp.told = 1.0e-6,
    sqp.tols = 1.0e-4,
    sqp.rpf = 1.0e-4,
    lbfgsb.REPORT = 10,
    lbfgsb.lmm = 20,
    lbfgsb.pgtol = 1e-14,
    lbfgsb.factr = 1,
    lbfgsb.fnscale = FALSE,
    lbfgsb.parscale = FALSE,
    nm.ndeps = 1e-14,
    nm.maxit = 10000,
    nm.abstol = 1e-14,
    nm.reltol = 1e-14,
    nm.alpha = 1.0,
    nm.beta = 0.5,
    nm.gamma = 2.0,
    nm.fnscale = FALSE,
    nm.parscale = FALSE)

Arguments

• llh: llh = c("filter", "internal", "testing")[1], defaults to "filter".

• nlminb.eval.max: maximum number of evaluations of the objective function, defaults to 200.

• nlminb.iter.max: maximum number of iterations, defaults to 150.

• nlminb.abs.tol: absolute tolerance, defaults to 1e-20.

• nlminb.rel.tol: relative tolerance, defaults to 1e-10.

• nlminb.x.tol: X tolerance, defaults to 1.5e-8.

• nlminb.fscale: defaults to FALSE.

• nlminb.xscale: defaulkts to FALSE.

• nlminb.step.min: minimum step size, defaults to 2.2e-14.

• nlminb.scale: defaults to 1.

• sqp.mit: maximum number of iterations, defaults to 200.

• sqp.mfv: maximum number of function evaluations, defaults to 500.

• sqp.met: specifies scaling strategy:

  sqp.met=1 - no scaling,

  sqp.met=2 - preliminary scaling in 1st iteration (default),

  sqp.met=3 - controlled scaling,

  sqp.met=4 - interval scaling,

  sqp.met=5 - permanent scaling in all iterations.

• sqp.mec: correction for negative curvature:

  sqp.mec=1 - no correction,

  sqp.mec=2 - Powell correction (default).

• sqp.mer: restarts after unsuccessful variable metric updates:

  sqp.mer=0 - no restarts,

  sqp.mer=1 - standard restart.

• sqp.mes: interpolation method selection in a line search:

  sqp.mes=1 - bisection,

  sqp.mes=2 - two point quadratic interpolation,

  sqp.mes=3 - three point quadratic interpolation,

  sqp.mes=4 - three point cubic interpolation (default).

• sqp.xmax: maximum stepsize, defaults to 1.0e+3.

• sqp.tolx: tolerance for the change of the coordinate vector, defaults to 1.0e-16.

• sqp.tolc: tolerance for the constraint violation, defaults to 1.0e-6.

• sqp.tolg: tolerance for the Lagrangian function gradient, defaults to 1.0e-6.

• sqp.told: defaults to 1.0e-6.

• sqp.tols: defaults to 1.0e-4.

• sqp.rpf: value of the penalty coefficient, default to1.0D-4. The default velue may be relatively small. Therefore, larger value, say one, can sometimes be more suitable.

• lbfgsb.REPORT: the frequency of reports for the "BFGS" and "L-BFGS-B"

  methods if control$trace is positive. Defaults to every 10 iterations.

• lbfgsb.lmm: an integer giving the number of BFGS updates retained in the "L-BFGS-B" method, It defaults to 5.

• lbfgsb.factr: controls the convergence of the "L-BFGS-B"

  method. Convergence occurs when the reduction in the objective is within this factor of the machine tolerance. Default is 1e7, that is a tolerance of about 1.0e-8.

• lbfgsb.pgtol: helps control the convergence of the "L-BFGS-B" method. It is a tolerance on the projected gradient in the current search direction. This defaults to zero, when the check is suppressed.

• lbfgsb.fnscale: defaults to FALSE.

• lbfgsb.parscale: defaults to FALSE.

• nm.ndeps: a vector of step sizes for the finite-difference approximation to the gradient, on par/parscale scale. Defaults to 1e-3.

• nm.maxit: the maximum number of iterations. Defaults to 100 for the derivative-based methods, and 500 for "Nelder-Mead". For "SANN" maxit gives the total number of function evaluations. There is no other stopping criterion. Defaults to 10000.

• nm.abstol: the absolute convergence tolerance. Only useful for non-negative functions, as a tolerance for reaching zero.

• nm.reltol: relative convergence tolerance. The algorithm stops if it is unable to reduce the value by a factor of reltol * (abs(val) + reltol) at a step. Defaults to sqrt(.Machine$double.eps), typically about 1e-8.

• nm.alpha, nm.beta, nm.gamma: scaling parameters for the "Nelder-Mead" method. alpha is the reflection factor (default 1.0), beta the contraction factor (0.5), and gamma the expansion factor (2.0).

• nm.fnscale: an overall scaling to be applied to the value of fn and gr during optimization. If negative, turns the problem into a maximization problem. Optimization is performed on fn(par) / nm.fnscale.

• nm.parscale: a vector of scaling values for the parameters. Optimization is performed on par/parscale and these should be comparable in the sense that a unit change in any element produces about a unit change in the scaled value.

Returns

a list

Author(s)

Diethelm Wuertz for the Rmetrics -port,

R Core Team for the 'optim' -port,

Douglas Bates and Deepayan Sarkar for the 'nlminb' -port,

Bell-Labs for the underlying PORT Library,

Ladislav Luksan for the underlying Fortran SQP Routine,

Zhu, Byrd, Lu-Chen and Nocedal for the underlying L-BFGS-B Routine.

See Also

garchFit

Examples

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