Description Usage Arguments Value Note Author(s) References See Also Examples

Fit a log-GARCH model by either (nonlinear) Least Squares (LS) or Quasi Maximum Likelihood (QML) via the ARMA representation. For QML either the Gaussian or centred exponential chi-squared distribution can be used as instrumental density, see Sucarrat, Gronneberg and Escribano (2013), and Francq and Sucarrat (2013). Zero-values on the dependent variable y are treated as missing values, as suggested in Sucarrat and Escribano (2013). Estimation is via the `nlminb`

function, whereas a numerical estimate of the Hessian is obtained with `optimHess`

for the computation of the variance-covariance matrix

1 2 3 4 5 |

`y` |
numeric vector, typically a financial return series or the error of a regression |

`arch` |
the arch order (i.e. an integer equal to or greater than 0). The default is 1. NOTE: in the current version the order canno be greater than 1 |

`garch` |
the garch order (i.e. an integer equal to or greater than 0). The default is 1. NOTE: in the current version the order canno be greater than 1 |

`xreg` |
vector or matrix with conditioning variables |

`initial.values` |
NULL (default) or a vector with the initial values of the ARMA-representation |

`lower` |
NULL (default) or a vector with the lower bounds of the parameter space (of the ARMA-representation). If NULL, then the values are automatically chosen |

`upper` |
NULL (default) or a vector with the upper bounds of the parameter space (of the ARMA-representation). If NULL, then the values are automatically chosen |

`nlminb.control` |
list of control options passed on to the |

`vcov` |
logical. If TRUE (default), then the variance-covariance matrix is computed. The FALSE options makes estimation faster, but the variance-covariance matrix cannot be extracted subsequently |

`method` |
Estimation method to use. Either "ls", i.e. Nonlinear Least Squares (default), "ml", i.e. Gaussian QML or "cex2", i.e. Centred exponential Chi-squared QML, see Francq and Sucarrat (2013). Note: For the cex2 method mean-correction = FALSE is not available |

`mean.correction` |
Whether to mean-correct the ARMA representation. Mean-correction is usually faster, but not always recommended if covariates are added (i.e. if xreg is not NULL) |

`objective.penalty` |
NULL (default) or a numeric value. If NULL, then the log-likelihood value associated with the initial values is used. Sometimes estimation can result in NA and/or +/-Inf values (this can be fatal for simulations). The value objective.penalty is the value returned by the objective function |

`solve.tol` |
The function |

`c.code` |
logical. TRUE (default) is (much) faster, since it makes use of compiled C-code in the recursions |

A list of class 'lgarch'

Empty

Genaro Sucarrat, http://www.sucarrat.net/

Francq, C. and G. Sucarrat (2013), 'An Exponential Chi-Squared QMLE for Log-GARCH Models via the ARMA Representation', MPRA Paper 51783: http://mpra.ub.uni-muenchen.de/51783/

Sucarrat and Escribano (2013), 'Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns', MPRA Paper 50699: http://mpra.ub.uni-muenchen.de/50699/

Sucarrat, Gronneberg and Escribano (2013), 'Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown', MPRA Paper 49344: http://mpra.ub.uni-muenchen.de/49344/

`lgarchSim`

, `coef.lgarch`

, `fitted.lgarch`

, `logLik.lgarch`

, `print.lgarch`

, `residuals.lgarch`

and `vcov.lgarch`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | ```
##simulate 500 observations w/default parameter values:
set.seed(123)
y <- lgarchSim(500)
##estimate a log-garch(1,1) w/least squares:
mymod <- lgarch(y)
##estimate the same model, but w/cex2 method:
mymod2 <- lgarch(y, method="cex2")
##print results:
print(mymod); print(mymod2)
##extract coefficients:
coef(mymod)
##extract Gaussian log-likelihood (zeros excluded) of the log-garch model:
logLik(mymod)
##extract Gaussian log-likelihood (zeros excluded) of the arma representation:
logLik(mymod, arma=TRUE)
##extract variance-covariance matrix:
vcov(mymod)
##extract and plot the fitted conditional standard deviation:
sdhat <- fitted(mymod)
plot(sdhat)
##extract and plot standardised residuals:
zhat <- residuals(mymod)
plot(zhat)
##extract and plot all the fitted series:
myhat <- fitted(mymod, verbose=TRUE)
plot(myhat)
``` |

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