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Type:

Package

Title:

Methods and Tools for Bayesian Dynamic Conditional Correlation GARCH(1,1) Model

Version:

3.0.4

Author:

Jose Augusto Fiorucci

[aut, cre, cph], Ricardo Sanders Ehlers

[aut, cph], Francisco Louzada

[aut, cph]

Maintainer:

Jose Augusto Fiorucci <jafiorucci@gmail.com>

Description:

Bayesian estimation of dynamic conditional correlation GARCH model for multivariate time series volatility (Fioruci, J.A., Ehlers, R.S. and Andrade-Filho, M.G., (2014). <doi:10.1080/02664763.2013.839635>.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

LazyData:

true

Depends:

R (≥ 2.0), numDeriv, coda

BugReports:

https://github.com/jafiorucci/bayesDccGarch/issues

URL:

https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract

NeedsCompilation:

yes

RoxygenNote:

7.1.2

Packaged:

2023-04-22 01:56:01 UTC; jafio

Repository:

CRAN

Date/Publication:

2023-04-22 07:20:02 UTC

bayesDccGARCH: Methods and tools for Bayesian analysis of DCC-GARCH(1,1) Model.

Description

In this package we implemented functions for Bayesian analysis of DCC-GARCH(1,1) Model using the same modelling of Fioruci et al (2014a). Several probabilities distributions are available for the errors which can model both skewness and heavy tails. See Fioruci et al (2014b) for more details about the package.

Details

Package:	bayesDccGarch
Type:	Package
Version:	3.0.4
Date:	2023-04-21
License:	GPL (>=2.14)

bayesDccGarch(mY, n_sim = 10000)

Author(s)

Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada. Maintainer: Jose Augusto Fiorucci <jafiorucci@gmail.com>

References

Fioruci, J.A., Ehlers, R.S., Andrade Filho, M.G. Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions, Journal of Applied Statistics, 41(2), 320–331, 2014a, <doi:10.1080/02664763.2013.839635>.

Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract

Examples



data(DaxCacNik)

out = bayesDccGarch(DaxCacNik)

summary(out)

plot(out)

Log-returns of daily indices of stock markets in Frankfurt, Paris and Tokio

Description

The matrix DaxCacNik contains daily observations of the hundredfold log-returns of daily indices of stock markets in Frankfurt (DAX), Paris (CAC40) and Tokyo (NIKKEI), from 10 October 1991 until 30 December 1997 (a total of 1627 days). The stock market data is freely available at https://robjhyndman.com/tsdldata/data/FVD1.dat.

Usage

data(DaxCacNik)

Author(s)

Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada

References

Fioruci, J.A., Ehlers, R.S. Andrade Filho, M.G. Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions, Journal of Applied Statistics, 41(2), 320–331, 2014. <doi:10.1080/02664763.2013.839635>

Bayesian Estimation of the DCC-GARCH(1,1) Model.

Description

Performs a Markov Chain for all parameters of the DCC-GARCH(1,1) Model.

Usage

bayesDccGarch(mY, nSim = 10000, tail_ini = 8, omega_ini=0.1*diag(var(mY)),
  alpha_ini=rep(0.05, ncol(mY)), beta_ini=rep(0.85, ncol(mY)),
	a_ini = 0.04, b_ini = 0.8, gamma_ini = rep(1, ncol(mY)),
	errorDist = 2, control = list())

increaseSim(x, nSim=10000)

## S3 method for class 'bayesDccGarch'
update(object, ..., mY_new)

## S3 method for class 'bayesDccGarch'
window(x, start = NULL, end = NULL, thin = NULL, ...)

Arguments

mY

a matrix of the data (n \times k).

nSim

length of Markov chain. Default: 10000.

tail_ini

initial value of \nu parameter if errorDist = 2 or initial value of \delta parameter if errorDist = 3. If errorDist = 1 this arguments is not used.

omega_ini

a numeric vector (k \times 1) with the initial values of \omega_i parameters. Default: rep(0.03, ncol(mY)).

alpha_ini

a numeric vector (k \times 1) with the initial values of \alpha_i parameters. Default: rep(0.03, ncol(mY)).

beta_ini

a numeric vector (k \times 1) with the initial values of \beta_i parameters. Default: rep(0.8, ncol(mY)).

a_ini

a numeric value of the initial values of a parameter. Default: 0.03.

b_ini

a numeric value of the initial values of b parameter. Default: 0.8.

gamma_ini

a numeric vector (k \times 1) with the initial values of \gamma_i parameters. Default: rep(1.0, ncol(mY)).

errorDist

a probability distribution for errors. Use errorDist=1 for SSNorm, errorDist=2 for SST or errorDist=3 for SSGED. Default: 2.

control

list of control arguments (See *Details*).

x, object

an object of bayesDccGarch class.

mY_new

a matrix of new data (n_{new} \times k).

start

the first iteration of interest from Markov chain.

end

the last iteration of interest from Markov chain.

thin

the required interval between successive samples.

...

additional arguments for S3 generic window function

Details

The bayesDccGarch() function performs a Markov Chain for all parameters of the model DCC-GARCH(1,1) (or GARCH(1,1) in the univariate case). There are three options of probability distributions for the error component. These are the standardized skew versions of normal, t-student and ged distributions. See Fioruci et al (2014a) and Fioruci et al (2014b) for any detail. The control argument can be used for define the prior hyper-parameters and the simulation algorithm parameters. It is a list that can supply any of the following components:

$mu_tail: the value of hyper-parameter \mu_\nu if errorDist=2 or the hyper-parameter \mu_\delta if errorDist=3. Default: 8
$mu_gamma: a vector with the hyper-parameters \mu_{\gamma_i}. Default: rep(0,ncol(mY)
$mu_omega: a vector with the hyper-parameters \mu_{\omega_i}. Default: rep(0,ncol(mY)
$mu_alpha: a vector with the hyper-parameters \mu_{\alpha_i}. Default: rep(0,ncol(mY)
$mu_beta: a vector with the hyper-parameters \mu_{\beta_i}. Default: rep(0,ncol(mY)
$mu_a: the value of the hyper-parameter \mu_a. Default: 0
$mu_b: the value of the hyper-parameter \mu_b. Default: 0
$sigma_tail: the value of hyper-parameter \sigma_\nu if errorDist=2 or the hyper-parameter \sigma_\delta if errorDist=3. Default: 10
$sigma_gamma: a vector with the hyper-parameters \sigma_{\gamma_i}. Default: rep(1.25,ncol(mY)
$sigma_omega: a vector with the hyper-parameters \sigma_{\omega_i}. Default: rep(10,ncol(mY)
$sigma_alpha: a vector with the hyper-parameters \sigma_{\alpha_i}. Default: rep(10,ncol(mY)
$sigma_beta: a vector with the hyper-parameters \sigma_{\beta_i}. Default: rep(10,ncol(mY)
$sigma_a: the value of the hyper-parameter \sigma_a. Default: 10
$sigma_b: the value of the hyper-parameter \sigma_b. Default: 10
$simAlg: the random walk Metropolis-Hasting algorithm update. Use 1 for update all parameters as one block, use 2 for update one parameter for each time and use 3 for an automatic choice.
$nPilotSim: number of simulation for pilot sample if control$simAlg=3. Default:1000
$cholCov: the cholesky decomposition matrix of the covariance matrix for simulation by one-block Metropolis-Hasting. It must to be passed if control$simAlg=1.
$sdSim: a vector with the standard deviations for simulation by one-dimensional Metropolis-Hasting. It must to be passed if control$simAlg=2.
$print: a logical variable for if the function should report the number of interactions in each 100 interactions or not. Default: TRUE

The function increaseSim() can be used to increase the length of Markov chain simulation.

The function window() can be used to filter the Markov chain simulation. In this case, all statistics are recomputed.

Value

An object of bayesDccGarch class, which contains a list with elements:

$control

a list with the used control argument.

$MC

an objetic of mcmc class with the Markov Chain simulation for all parameters. (R package coda)

$H

a matrix with the Bayesian estimates of volatilities and co-volatilities.

$R

a matrix with the estimates of the dynamic coditional correlation.

$H_n1

Bayesian prediction of volatilities and co-volatilities for y_n+1.

$R_n1

Bayesian prediction of coditional correlation for y_n+1.

$IC

the Bayesian estimate of Akaike Information Criterion, Bayesian Information Criterion and Deviance Information Criterion.

$elapsedTime

an object of class proc_time which is a numeric vector of length 5, containing the user, system, and total elapsed times of the process.

Author(s)

Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada

References

Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract.

Examples




data(DaxCacNik)

### Bayes DCC-GARCH(1,1) ###
mY = head(DaxCacNik, 1500)
out1 = bayesDccGarch(mY)
  # more 50000 simulations
out2 = increaseSim(out1, 50000)
  # remove first 10000 simulations and take at intervals of 20
out3 = window(out2, start=10000, thin = 20)
summary(out3)

# Plotting volatilities
plot(out3)

# Plotting Markov Chain
plot(out3$MC)

# Forecast volatility
H_pred = predict(out3, n_ahead=200)$H
plot.ts(rbind(out3$H, H_pred), main="volatility: historical and forecast")

# New data
out4 = update(out3, mY_new=DaxCacNik[1501:1628,])
plot(out4)

### Bayes univariate GARCH(1,1) ###
Dax = DaxCacNik[,1]
out = bayesDccGarch(Dax)
summary(out)
plot(out)

Density functions of multivariate Standard Skew Norm, t-Student and GED distributions

Description

Compute the density function of Standard Skew Normal distribution (SSNORM) or density function of Standard Skew t-Student distribution (SST) or density function of Standard Skew GED distribution (SSGED)

Usage

  dssnorm(x, gamma=rep(1,length(x)), log=FALSE)
  
  dsst(x, gamma=rep(1,length(x)), nu=10, log=FALSE)
  
  dssged(x, gamma=rep(1,length(x)), delta=2, log=FALSE)

Arguments

x

a numeric vector for the point which the density will be computed.

gamma

a numeric vector for skew parameters. Must be positive.

nu

a numeric value of shape parameter of the multivariate Standard Skew t-Student distribution. Must be greater than 2.

delta

a numeric value of shape parameter of GED distribution. Must be positive.

log

logical; if TRUE, densities p are returned as log(p).

Value

Returns the computed value of the density.

Author(s)

Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada

References

Examples

### Univariate symmetric standard norm distributions ###
dssnorm(x=0)
dsst(x=0, nu=100)
dssged(x=0, delta=2)

### Univariate standard skew norm distributions ###
dssnorm(x=0, gamma=1.5)
dsst(x=0, gamma=1.5, nu=100)
dssged(x=0, gamma=1.5, delta=2)

### Multivariate standard skew norm distributions ###
dssnorm(x=c(0,0), gamma=c(1.5,0.7))
dsst(x=c(0,0), gamma=c(1.5,0.7), nu=100)
dssged(x=c(0,0), gamma=c(1.5,0.7), delta=2)

The logarithm of likelihood function of DCC-GARCH(1,1) Model.

Description

Compute the logarithm of likelihood function of DCC-GARCH(1,1) Model if mY is a matrix or the logarithm of likelihood function of GARCH(1,1) Model if mY is numeric vector.

Usage

logLikDccGarch(mY, omega = rep(0.03, ncol(mY)), alpha = rep(0.03, ncol(mY)), 
	beta = rep(0.8, ncol(mY)), a = 0.03, b = 0.8, gamma = rep(1, ncol(mY)), 
	tail = 10, errorDist = 2)

Arguments

mY

a matrix of the data (n \times k).

omega

a numeric vector (k \times 1) with the the values of \omega_i parameters. Default: rep(0.03, ncol(mY)).

alpha

a numeric vector (k \times 1) with the the values of \alpha_i parameters. Default: rep(0.03, ncol(mY)).

beta

a numeric vector (k \times 1) with the the values of \beta_i parameters. Default: rep(0.80, ncol(mY)).

a

a numeric value of the a parameter. Default: 0.03.

b

a numeric value of the b parameter. Default: 0.8.

gamma

a numeric vector (k \times 1) with the values of \gamma_i parameters. Default: rep(1.0, ncol(mY)).

tail

a numeric value of \nu parameter if errorDist = 2 or of \delta parameter if errorDist = 3. If errorDist = 1 so this arguments is no used.

errorDist

a probability distribution for errors. Use errorDist=1 for SSNorm, errorDist=2 for SST or errorDist=3 for SSGED. Default: 2.

Details

The log-likelihood of the model GARCH(1,1) is computed if mY has just one column. The arguments a and b are not consider in this case.

Value

Return a list with the elements:

$H

a matrix where the lines are the H_t values for t=1,...,n.

$value

the value of the logarithm of likelihood function.

Author(s)

Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada

References

Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract.

Examples


data(DaxCacNik)

Dax = DaxCacNik[,1]

######  log-likelihood function of GARCH(1,1) model with SST innovations ####
logLikDccGarch(Dax, omega=0.03, alpha=0.03, beta=0.8, gamma=0.7)$value

######  log-likelihood function of DCC-GARCH(1,1) model with SST innovations ####
logLikDccGarch(DaxCacNik, beta=c(0.82,0.91,0.85), gamma=c(0.7, 1.3, 1.7), tail=10)$value

Plotting volatilities for Bayesian DCC-GARCH model

Description

Produces a plot of time series and the volatilities. This is a particular case of plotVol function.

Usage

## S3 method for class 'bayesDccGarch'
plot(x, ts.names=NULL, colors = c("grey","red"), ...)

Arguments

x

Object of class “bayesDccGarch”.

ts.names

a vector of length k with the names of the time series.

colors

a vector with the colors for plotting the returns and volatilities.

...

additional arguments for plot function

Value

No return value

Author(s)

Ricardo Sandes Ehlers, Jose Augusto Fiorucci and Francisco Louzada

References

Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract.

Examples



data(DaxCacNik)

mY = DaxCacNik

out = bayesDccGarch(mY, nSim=1000)
plot(out)

Plotting volatilities of time series

Description

Plotting method for volatilities of time series.

Usage

plotVol(mY, vol, ts.names=paste("TS_", 1:ncol(mY), sep=""), colors = c("grey","red"), ...)

Arguments

mY

a matrix of the data (n \times k).

vol

a matrix (n \times k) with the volatility estimates.

ts.names

a vector of length k with the names of the time series.

colors

a vector with name of the colors for plotting the returns and volatilities.

...

additional arguments for plot function

Value

No return value

Author(s)

Ricardo Sandes Ehlers, Jose Augusto Fiorucci and Francisco Louzada

References

Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract.

Examples



data(DaxCacNik)

mY = DaxCacNik

out = bayesDccGarch(mY)

## The code
plotVol(mY, out$H[,c("H_1,1","H_2,2","H_3,3")], c("DAX","CAC40","NIKKEI"))

## gives the result of ##
plot(out)

Bayesian forecast for volatilities and coditional correlations

Description

Bayesian forecast for volatilities and coditional correlations

Usage

## S3 method for class 'bayesDccGarch'
predict(object, ..., n_ahead = 5, bayes = T)

Arguments

object

a bayesDccGarch object

...

default argument of predict function, not used

n_ahead

number of steps ahead forecast

bayes

a boolean. If True, then the forecast is calculated as being the average of the forecasts across all states in the Markov chain (much slower). If False then predictions are calculated using estimation parameters (much faster).

Value

A list with elements H and R

References

Engle, R.F. and Sheppard, K. Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH, 2001, NBER Working Paper.

Examples


out = bayesDccGarch(DaxCacNik)
predict.bayesDccGarch(out, n_ahead=5)

bayesDccGARCH: Methods and tools for Bayesian analysis of DCC-GARCH(1,1) Model.

Description

Details

Author(s)

References

See Also

Examples

Log-returns of daily indices of stock markets in Frankfurt, Paris and Tokio

Description

Usage

Author(s)

References

Bayesian Estimation of the DCC-GARCH(1,1) Model.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Density functions of multivariate Standard Skew Norm, t-Student and GED distributions

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

The logarithm of likelihood function of DCC-GARCH(1,1) Model.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plotting volatilities for Bayesian DCC-GARCH model

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Plotting volatilities of time series

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Bayesian forecast for volatilities and coditional correlations

Description

Usage

Arguments

Value

References

Examples