lgarch: Estimate a log-GARCH model
In lgarch: Simulation and Estimation of Log-GARCH Models

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

lgarch(y, arch = 1, garch = 1, xreg = NULL, initial.values = NULL,
  lower = NULL, upper = NULL, nlminb.control = list(), vcov = TRUE,
  method=c("ls","ml","cex2"), mean.correction=FALSE,
  objective.penalty = NULL, solve.tol = .Machine$double.eps,
  c.code = TRUE)

`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 `nlminb` optimiser
`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 `lgarchObjective` in the presence of NA or +/-Inf values
`solve.tol`	The function `solve` is used for the inversion of the negative of the Hessian in computing the variance-covariance matrix. The value solve.tol is passed on to `solve`, and is the tolerance for detecting linear dependencies in the columns
`c.code`	logical. TRUE (default) is (much) faster, since it makes use of compiled C-code in the recursions

A list of class 'lgarch'

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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

##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)

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric


Date: Wed May 15 10:36:05 2019 
Method: LS 
Message (nlminb): relative convergence (4) 
No. of observations: 500 
Sample: 1 to 500 

Coefficients:
             intercept      arch1    garch1      Elnz2
Estimate:   -0.2929861 0.04273328 0.7082512 -1.2657802
Std. Error:         NA 0.03313073 0.2178691  0.0716916
                                     
Log-likelihood (log-garch):  -361.026
Log-likelihood (arma):      -1085.667
Sum Squared Resids. (arma):    2251.6
No. of non-zeros:                 500
No. of zeros:                       0


Date: Wed May 15 10:36:05 2019 
Method: CEX2 (w/mean-correction) 
Message (nlminb): relative convergence (4) 
No. of observations: 500 
Sample: 1 to 500 

Coefficients:
             intercept      arch1    garch1       Elnz2
Estimate:   -0.4915509 0.04258921 0.5633112 -1.27634643
Std. Error:         NA 0.02213739 0.1945688  0.06348243
                                     
Log-likelihood (log-garch):  -361.369
Log-likelihood (arma):      -1026.757
Sum Squared Resids. (arma):   2254.15
No. of non-zeros:                 500
No. of zeros:                       0

  intercept       arch1      garch1       Elnz2 
-0.29298607  0.04273328  0.70825122 -1.26578023 
'log Lik.' -361.0257 (df=3)
'log Lik.' -1085.667 (df=3)
          intercept        arch1      garch1       Elnz2
intercept        NA           NA          NA          NA
arch1            NA  0.001097645 -0.00325630          NA
garch1           NA -0.003256300  0.04746696          NA
Elnz2            NA           NA          NA 0.005139685