Description Details Author(s) References See Also Examples

This package provides facilities for the simulation and estimation of univariate log-GARCH models, and for the multivariate CCC-log-GARCH(1,1) model, see Sucarrat, Gronneberg and Escribano (2013), Sucarrat and Escribano (2013), and Francq and Sucarrat (2013).

Let y[t] denote a financial return or the error of a regression at time t such that

y[t] = sigma[t]*z[t],

where sigma[t] > 0 is the conditional standard deviation or volatility at t, and where z[t] is an IID innovation with mean zero and unit variance. The log-volatility specifiction of the log-GARCH-X model is given by

ln sigma[t]^2 = intercept + Sum_i alpha_i * ln y[t-i]^2 + Sum_j beta_j *ln sigma[t-1]^2 + Sum_k lambda_k * x[t]_k,

where the conditioning x-variables can be contemporaneous and/or lagged. The lgarch package estimates this model via its ARMA-X representation, see Sucarrat, Gronneberg and Escribano (2013), and treats zeros on y as missing values, see Sucarrat and Escribano (2013).

Package: | lgarch |

Type: | Package |

Version: | 0.6-2 |

Date: | 2015-09-14 |

License: | GPL-2 |

LazyLoad: | yes |

The main functions of the package are: `lgarchSim`

, `mlgarchSim`

, `lgarch`

and `mlgarch`

. The first two functions simulate from a univariate and a multivariate log-GARCH model, respectively, whereas the latter two estimate a univariate and a multivariate log-GARCH model, respectively.

The lgarch and mlgarch functions return an object (a list) of class 'lgarch' and 'mlgarch', respectively. In both cases a collection of methods can be applied to each of them: coef, fitted, logLik, print, residuals, summary and vcov. In addition, the function `rss`

can be used to extract the Residual Sum of Squares of the estimated ARMA representation from an lgarch object.

The output produced by the `lgarchSim`

and `mlgarchSim`

functions, and by the fitted and residuals methods, are of the Z's ordered observations (`zoo`

) class, see Zeileis and Grothendieck (2005), and Zeileis, Grothendieck and Ryan (2014). This means a range of time-series and plotting methods are available for these objects.

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, G. and A. 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, G., S. Gronneberg and A. 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/

Zeileis, A. and G. Grothendieck (2005), 'zoo: S3 Infrastructure for Regular and Irregular Time Series', Journal of Statistical Software 14, pp. 1-27

Zeileis, A., G. Grothendieck, J.A. Ryan and F. Andrews(2014), 'zoo: S3 Infrastructure for Regular and Irregular Time Series (Z's ordered observations)', R package version 1.7-11, http://CRAN.R-project.org/package=zoo/

`lgarchSim`

, `mlgarchSim`

, `lgarch`

, `mlgarch`

, `coef.lgarch`

, `coef.mlgarch`

, `fitted.lgarch`

,

`fitted.mlgarch`

, `logLik.lgarch`

, `logLik.mlgarch`

, `print.lgarch`

, `print.mlgarch`

,

`residuals.lgarch`

, `residuals.mlgarch`

, `rss`

, `summary.mlgarch`

, `summary.mlgarch`

, `vcov.lgarch`

,

`vcov.mlgarch`

and `zoo`

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 37 38 39 40 41 42 43 44 45 | ```
##simulate 500 observations w/default parameter values from
##a univariate log-garch(1,1):
set.seed(123)
y <- lgarchSim(500)
##estimate a log-garch(1,1):
mymod <- lgarch(y)
##print results:
print(mymod)
##extract coefficients:
coef(mymod)
##extract Gaussian log-likelihood (zeros excluded, if any) of the log-garch model:
logLik(mymod)
##extract Gaussian log-likelihood (zeros excluded, if any) 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)
##simulate 1000 observations from a two-dimensional
##ccc-log-garch(1,1) w/default parameter values:
set.seed(123)
yy <- mlgarchSim(1000)
##estimate a 2-dimensional ccc-log-garch(1,1):
myymod <- mlgarch(yy)
##print results:
print(myymod)
``` |

lgarch documentation built on May 29, 2017, 9:08 a.m.

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