Package 'garchx' reference manual

Title:	Flexible and Robust GARCH-X Modelling
Description:	Flexible and robust estimation and inference of generalised autoregressive conditional heteroscedasticity (GARCH) models with covariates ('X') based on the results by Francq and Thieu (2018) <doi:10.1017/S0266466617000512>. Coefficients can straightforwardly be set to zero by omission, and quasi maximum likelihood methods ensure estimates are generally consistent and inference valid, even when the standardised innovations are non-normal and/or dependent over time, see <https://journal.r-project.org/archive/2021/RJ-2021-057/RJ-2021-057.pdf> for an overview of the package.
Authors:	Genaro Sucarrat [aut, cre]
Maintainer:	Genaro Sucarrat <[email protected]>
License:	GPL (>= 2)
Version:	1.5
Built:	2024-12-24 03:12:16 UTC
Source:	https://github.com/gsucarrat/garchx

Flexible and Robust GARCH-X Modelling

Description

Flexible and robust estimation and inference of GARCH(q,p,r)-X models, where q is the GARCH order, p is the ARCH order, r is the asymmetry or leverage order, and 'X' indicates that covariates can be included. Suitable subsets of the coefficients can be restriced to zero by omission, and Quasi Maximum Likelihood (QML) methods ensure estimates are generally consistent, even when the standardised innovations are non-normal and/or dependent.

Details

Package:	garchx
Type:	Package
Version:	1.5
Date:	2022-09-13
License:	GPL-2

Author(s)

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

Maintainer: Genaro Sucarrat

Examples

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)
mymod

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)
mymod

Extraction functions for 'garchx' objects

Description

Extraction functions for objects of class 'garchx'

Usage

  ## S3 method for class 'garchx'
coef(object, ...)
  ## S3 method for class 'garchx'
fitted(object, as.zoo = TRUE, ...)
  ## S3 method for class 'garchx'
logLik(object, ...)
  ## S3 method for class 'garchx'
nobs(object, ...)
  ## S3 method for class 'garchx'
predict(object, n.ahead = 10, newxreg = NULL,
    newindex = NULL, n.sim = NULL, verbose = FALSE, ...)
  ## S3 method for class 'garchx'
print(x, ...)
  ## S3 method for class 'garchx'
quantile(x, probs=0.025, names = TRUE, type = 7, as.zoo = TRUE, ...)
  ## S3 method for class 'garchx'
residuals(object, as.zoo = TRUE, ...)
  ## S3 method for class 'garchx'
toLatex(object, digits = 4, ...)
  ## S3 method for class 'garchx'
vcov(object, vcov.type = NULL, ...)
## S3 method for class 'garchx'
coef(object, ...)
  ## S3 method for class 'garchx'
fitted(object, as.zoo = TRUE, ...)
  ## S3 method for class 'garchx'
logLik(object, ...)
  ## S3 method for class 'garchx'
nobs(object, ...)
  ## S3 method for class 'garchx'
predict(object, n.ahead = 10, newxreg = NULL,
    newindex = NULL, n.sim = NULL, verbose = FALSE, ...)
  ## S3 method for class 'garchx'
print(x, ...)
  ## S3 method for class 'garchx'
quantile(x, probs=0.025, names = TRUE, type = 7, as.zoo = TRUE, ...)
  ## S3 method for class 'garchx'
residuals(object, as.zoo = TRUE, ...)
  ## S3 method for class 'garchx'
toLatex(object, digits = 4, ...)
  ## S3 method for class 'garchx'
vcov(object, vcov.type = NULL, ...)

Arguments

`object`	an object of class 'garchx'
`x`	an object of class 'garchx'
`as.zoo`	logical. If `TRUE`, then the returned result is of class `zoo`
`n.ahead`	`integer` that determines how many steps ahead predictions should be generated
`newxreg`	`vector` or `matrix` with the out-of-sample regressor values
`newindex`	`zoo`-index for the out-of-sample predictions. If `NULL` (default), then `1:n.ahead` is used
`n.sim`	`NULL` or an `integer`, the number of simulations
`verbose`	`logical`. If `TRUE`, then the simulations - in addition to the predictions - are returned
`probs`	`vector` of probabilities
`names`	`logical`, whether to return names or not
`type`	`integer` that determines the algorithm used to compute the quantile, see `quantile`
`digits`	`integer`, the number of digits in the printed LaTeX code
`vcov.type`	`NULL` or a `character` that is (partially) matched to `"ordinary"` or `"robust"`. The robust coefficient-covariance is that of Francq and Thieu (2018).
`...`	additional arguments

Value

`coef:`	numeric vector containing parameter estimates
`fitted:`	fitted conditional variance
`logLik:`	log-likelihood (normal density)
`nobs:`	the number of observations used in the estimation
`predict:`	a `vector` with the predictions (`verbose=FALSE`), or a `matrix` with both the predictions and the simulations (`verbose=TRUE`)
`print:`	print of the estimation results
`quantile:`	the fitted quantiles, i.e. the conditional standard deviation times the empirical quantile of the standardised innovations
`residuals:`	standardised residuals
`vcov:`	coefficient variance-covariance matrix

Author(s)

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

References

Christian Francq and Le Quien Thieu (2018): 'QML inference for volatility models with covariates', Econometric Theory, doi:10.1017/S0266466617000512

Examples

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)

##print estimation results:
print(mymod)

##extract coefficients:
coef(mymod)

##extract and store conditional variances:
sigma2hat <- fitted(mymod)

##extract log-likelihood:
logLik(mymod)

##extract and store standardised residuals:
etahat <- residuals(mymod)

##extract coefficient variance-covariance matrix:
vcov(mymod)

##generate predictions:
predict(mymod)

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)

##print estimation results:
print(mymod)

##extract coefficients:
coef(mymod)

##extract and store conditional variances:
sigma2hat <- fitted(mymod)

##extract log-likelihood:
logLik(mymod)

##extract and store standardised residuals:
etahat <- residuals(mymod)

##extract coefficient variance-covariance matrix:
vcov(mymod)

##generate predictions:
predict(mymod)

Estimate a GARCH-X model

Description

Quasi Maximum Likelihood (ML) estimation of a GARCH(q,p,r)-X model, where q is the GARCH order, p is the ARCH order, r is the asymmetry (or leverage) order and 'X' indicates that covariates can be included. Note that the underlying estimation theory assumes the covariates are stochastic. The estimation procedure will, in general, provide consistent estimates when the standardised innovations are not normal or independent (or both), see Francq and Thieu (2018).

Usage

garchx(y, order = c(1,1), arch = NULL, garch = NULL, asym = NULL,
  xreg = NULL, vcov.type = c("ordinary", "robust"),
  initial.values = NULL, backcast.values = NULL, lower = 0,
  upper = +Inf, control = list(), hessian.control = list(),
  solve.tol = .Machine$double.eps, estimate = TRUE, c.code = TRUE,
  penalty.value = NULL, sigma2.min = .Machine$double.eps,
  objective.fun = 1, turbo = FALSE)
garchx(y, order = c(1,1), arch = NULL, garch = NULL, asym = NULL,
  xreg = NULL, vcov.type = c("ordinary", "robust"),
  initial.values = NULL, backcast.values = NULL, lower = 0,
  upper = +Inf, control = list(), hessian.control = list(),
  solve.tol = .Machine$double.eps, estimate = TRUE, c.code = TRUE,
  penalty.value = NULL, sigma2.min = .Machine$double.eps,
  objective.fun = 1, turbo = FALSE)

Arguments

`y`	numeric vector, time-series or `zoo` object. Missing values in the beginning and at the end of the series is allowed, as they are removed with the `na.trim` command
`order`	integer vector of length 1, 2 or 3, for example `c(1,1,1)`. The first entry controls the GARCH order, the second the ARCH order and the third the ASYM (asymmetry/leverage) order
`arch`	`NULL` or numeric vector containing the ARCH-terms to include. Note: If not `NULL`, then the value of the `ARCH` argument overrides the value of the first entry in the `order` argument
`garch`	`NULL` or numeric vector containing the GARCH-terms to include. Note: If not `NULL`, then the value of the `GARCH` argument overrides the value of the second entry in the `order` argument
`asym`	`NULL` or numeric vector containing the ASYM-terms (asymmetry/leverage terms) to include. Note: If not `NULL`, then the value of the `ASYM` argument overrides the value of the third entry in the `order` argument
`xreg`	numeric vector, time-series or `zoo` object. Missing values in the beginning and at the end of the series is allowed, as they are removed with the `na.trim` command
`vcov.type`	`character`, either `"ordinary"` or `"robust"`, see `vcov.garchx`
`initial.values`	`NULL` or a numeric vector with the initial parameter values passed on to the optimisation routine, `nlminb`. If `NULL`, the default, then the values are chosen automatically
`backcast.values`	`NULL` or a non-negative numeric. The backcast value is used to initiate the forward recursion of the conditional variance. If `NULL` (default), then the value is chosen automatically (currently the average of `y` squared is used). If `backcast.values` is a non-negative numeric, then the initial recursion values are all set to this value
`lower`	numeric vector, either of length 1 or the number of parameters to be estimated, see `nlminb`
`upper`	numeric vector, either of length 1 or the number of parameters to be estimated, see `nlminb`
`control`	a `list` passed on to the `control` argument of `nlminb`
`hessian.control`	a `list` passed on to the `control` argument of `optimHess`
`solve.tol`	numeric value passed on to the `tol` argument of `solve`, which is called whenever the coefficient variance-coariance matrix is computed. The value controls the toleranse for detecting linear dependence between columns when inverting a matrix
`estimate`	logical, if `TRUE` then estimation is carried out. If `FALSE`, then the `initial.values` are used
`c.code`	logical, if `TRUE` then compiled C code is used in the forward recursion
`penalty.value`	`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. The `penalty.value` is the value returned by the objective function `garchxObjective` in the presence of `NA` or `+/-Inf` values
`sigma2.min`	numeric with default `.Machine$double.eps`. To avoid taking taking the log of a very small value when computing the log-likelihood, `sigma2.min` is used as the lower bound of the fitted conditional variances, see the code of `garchxObjective`
`objective.fun`	numeric, either 1 or 0
`turbo`	logical. If `FALSE` (default), then the coefficient variance-covariance is computed during estimation, and the fitted values and residuals are attached to the returned object. If `TRUE`, then these operations are skipped, and hence estimation is faster. Note, however, that if `turbo` is set to `TRUE`, then the coefficient-covariance, fitted values and residuals can still be extracted subsequent to estimation with `vcov.garchx`, `fitted.garchx` and `residuals.garchx`, respectively

Value

A list of class 'garchx'

Author(s)

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

References

Christian Francq and Le Quien Thieu (2018): 'QML inference for volatility models with covariates', Econometric Theory, doi:10.1017/S0266466617000512
Christian Francq and Jean-Michel Zakoian (2019): 'GARCH Models', 2nd Edition, Wiley

Examples

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)

##print estimation results:
print(mymod)

##extract coefficients:
coef(mymod)

##extract and store conditional variances:
sigma2hat <- fitted(mymod)

##extract log-likelihood:
logLik(mymod)

##extract and store standardised residuals:
etahat <- residuals(mymod)

##extract variance-covariance matrix:
vcov(mymod)

##generate predictions:
predict(mymod)

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)

##print estimation results:
print(mymod)

##extract coefficients:
coef(mymod)

##extract and store conditional variances:
sigma2hat <- fitted(mymod)

##extract log-likelihood:
logLik(mymod)

##extract and store standardised residuals:
etahat <- residuals(mymod)

##extract variance-covariance matrix:
vcov(mymod)

##generate predictions:
predict(mymod)

Asymptotic Coefficient Covariance

Description

Compute the asymptotic coefficient-covariance of a GARCH(q,p,r)-X model by simulation. Note that the principles of how to use the arch, garch, asym and xreg arguments are the same as those of garchx

Usage

garchxAvar(pars, arch = NULL, garch = NULL, asym = NULL,
  xreg = NULL, vcov.type = c("ordinary", "robust"),
  innovations = NULL, Eeta4 = NULL, n = 1e+06, objective.fun = 1,
  seed = NULL)
garchxAvar(pars, arch = NULL, garch = NULL, asym = NULL,
  xreg = NULL, vcov.type = c("ordinary", "robust"),
  innovations = NULL, Eeta4 = NULL, n = 1e+06, objective.fun = 1,
  seed = NULL)

Arguments

`pars`	`vector` of parameters of length 1 or more. The first component contains the coefficient-value of the intercept, the next component(s) the ARCH-coefficient(s), and so on.
`arch`	`NULL` or integer `vector` with the lags of the ARCH-terms to include. Works in the same way as the `arch` argument in the `garchx` function
`garch`	`NULL` or integer `vector` with the lags of the GARCH-terms. Works in the same way as the `garch` argument in the `garchx` function
`asym`	`NULL` or integer `vector` with the lags of the asymmetry terms to include. Works in the same way as the `asym` argument in the `garchx` function
`xreg`	`NULL`, or a `vector` or `matrix` with the covariates of the model. Works in the same way as the `xreg` argument in the `garchx` function
`vcov.type`	`character` that determines the type of coefficient-covariance
`innovations`	`NULL` or a `vector` with the standardised innovations to use. If `NULL`, then the innovations are standard normal
`Eeta4`	`numeric`, the fourth moment of the innovations. If `NULL`, then the value is estimated internally. Note: The value of Eeta4 is only used if `vcov.type = "ordinary"`, otherwise it is ignored
`n`	integer, the number of observations to use in the simulations
`objective.fun`	integer equal to 1 or 0 that determines the type of objective function to use, see the code of `garchxObjective`
`seed`	`NULL` or an integer that sets the seed (the value is passed on to `set.seed`. Useful for reproducibility

Value

A matrix

Author(s)

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

References

Christian Francq and Le Quien Thieu (2018): 'QML inference for volatility models with covariates', Econometric Theory, doi:10.1017/S0266466617000512 Christian Francq and Jean-Michel Zakoian (2019): 'GARCH Models', 2nd Edition, Wiley

Examples


##asymptotic coefficient-covariance of a garch(1,1)
##note: the estimate is rough, since n is small
intercept <- 0.2
alpha <- 0.1
beta <- 0.8
pars <- c(intercept, alpha, beta)
seed <- 123 #for reproducibility
garchxAvar(pars, arch=1, garch=1, n=10000, seed=seed)

##asymptotic coefficient-covariance of a garch(1,1)
##note: the estimate is rough, since n is small
intercept <- 0.2
alpha <- 0.1
beta <- 0.8
pars <- c(intercept, alpha, beta)
seed <- 123 #for reproducibility
garchxAvar(pars, arch=1, garch=1, n=10000, seed=seed)

Auxiliary functions

Description

Auxiliary functions used in estimation. Not intended for the average user

Usage

  garchxObjective(pars, aux)
  garchxRecursion(pars, aux)
garchxObjective(pars, aux)
  garchxRecursion(pars, aux)

Arguments

`pars`	numeric vector of parameters
`aux`	`list` created by `garchx`

Value

`garchxObjective:`	value of the objective function
`garchxRecursion:`	fitted conditional variance

Author(s)

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

Simulate from a GARCH-X model

Description

Simulate from a GARCH(q,p,r)-X model. Optionally, if verbose=TRUE, the conditional variance and innovations are also returned.

Usage

garchxSim(n, intercept = 0.2, arch = 0.1, garch = 0.8, asym = NULL, xreg = NULL,
  innovations = NULL, backcast.values = list(), verbose = FALSE, as.zoo = TRUE,
  c.code = TRUE)
garchxSim(n, intercept = 0.2, arch = 0.1, garch = 0.8, asym = NULL, xreg = NULL,
  innovations = NULL, backcast.values = list(), verbose = FALSE, as.zoo = TRUE,
  c.code = TRUE)

Arguments

`n`	integer
`intercept`	numeric
`arch`	`NULL` or numeric vector with the values of the ARCH-coefficients
`garch`	`NULL` or numeric vector with the values of the GARCH-coefficients
`asym`	`NULL` or numeric vector with the values of the asymmetry-coefficients
`xreg`	`NULL` or numeric vector with the values of the X-term
`innovations`	`NULL` or numeric vector with the innovations. If `NULL`, then standard normal innovations are generated with `rnorm`
`backcast.values`	`list` with backcast values
`verbose`	`logical`
`as.zoo`	`logical`. If `TRUE` (default), then the returned object is of class `zoo`
`c.code`	`logical`. If `TRUE` (default), then compiled C code is used for the recursion (faster). Otherwise R code is used (slower)

Value

a numeric vector or matrix with the simulated values.

Author(s)

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

Examples

##simulate from a garch(1,1):
y <- garchxSim(1000)

##simulate from a garch(1,1) with asymmetry/leverage:
yy <- garchxSim(1000, asym=0.1)

##simulate from a garch(1,1) w/user-provided backcast values:
yyy <- garchxSim(1000, backcast.values=list(z2=1, sigma2=0.5))

##simulate from a garch(1,1):
y <- garchxSim(1000)

##simulate from a garch(1,1) with asymmetry/leverage:
yy <- garchxSim(1000, asym=0.1)

##simulate from a garch(1,1) w/user-provided backcast values:
yyy <- garchxSim(1000, backcast.values=list(z2=1, sigma2=0.5))

Difference a vector or a matrix, with special treatment of zoo objects

Description

Similar to the diff function from the base package, but gdiff enables padding (e.g. NAs or 0s) of the lost entries. Contrary to the diff function in the base package, however, the default in gdiff is to pad (with NAs). The gdiff function is particularly suited for zoo objects, since their indexing is retained

Usage

gdiff(x, lag = 1, pad = TRUE, pad.value = NA)
gdiff(x, lag = 1, pad = TRUE, pad.value = NA)

Arguments

`x`	a numeric vector or matrix
`lag`	integer equal to the difference-length (the default is 1)
`pad`	logical. If `TRUE` (default), then the lost entries are padded with pad.value. If `FALSE`, then no padding is undertaken
`pad.value`	numeric, the pad-value

Value

A vector or matrix with the differenced values

Note

Empty

Author(s)

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

Examples

##1st difference of a series:
x <- rnorm(5)
gdiff(x)

##1st difference with no padding:
gdiff(x, pad=FALSE)

##1st difference retaining the original zoo-index ordering:
gdiff(as.zoo(x))

##1st difference of a matrix:
y <- matrix(rnorm(8),4,2)
gdiff(y)

##2nd difference of the same matrix:
gdiff(y, lag=2)

##1st difference of a series:
x <- rnorm(5)
gdiff(x)

##1st difference with no padding:
gdiff(x, pad=FALSE)

##1st difference retaining the original zoo-index ordering:
gdiff(as.zoo(x))

##1st difference of a matrix:
y <- matrix(rnorm(8),4,2)
gdiff(y)

##2nd difference of the same matrix:
gdiff(y, lag=2)

Lag a vector or a matrix, with special treatment of `zoo` objects

Description

Similar to the lag function from the stats package, but glag enables padding (e.g. NAs or 0s) of the lost entries. Contrary to the lag function in the stats package, however, the default in glag is to pad (with NAs). The glag is particularly suited for zoo objects, since their indexing is retained

Usage

glag(x, k = 1, pad = TRUE, pad.value = NA)
glag(x, k = 1, pad = TRUE, pad.value = NA)

Arguments

`x`	a numeric vector or matrix
`k`	integer equal to the lag (the default is 1)
`pad`	logical. If TRUE (default), then the lost entries are padded with pad.value. If FALSE, then no padding is undertaken
`pad.value`	the pad-value

Value

A vector or matrix with the lagged values

Note

Empty

Author(s)

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

Examples

##lag series with NA for the missing entries:
x <- rnorm(5)
glag(x)

##lag series with no padding:
x <- rnorm(5)
glag(x, pad=FALSE)

##lag series and retain the original zoo-index ordering:
x <- as.zoo(rnorm(5))
glag(x)

##lag two periods:
glag(x, k=2)

##lag series with NA for the missing entries:
x <- rnorm(5)
glag(x)

##lag series with no padding:
x <- rnorm(5)
glag(x, pad=FALSE)

##lag series and retain the original zoo-index ordering:
x <- as.zoo(rnorm(5))
glag(x)

##lag two periods:
glag(x, k=2)

Refit a model to new data

Description

Refit a model to new data, typically for cross-validation purposes. Re-estimation (reestimate) is optional (the default is FALSE).

Usage

##generic:
refit(object, ...)

##S3 method for 'garchx' objects:
## S3 method for class 'garchx'
refit(object, newy = NULL, newxreg = NULL,
  backcast.value = NULL, reestimate = FALSE, ...)

##generic:
refit(object, ...)

##S3 method for 'garchx' objects:
## S3 method for class 'garchx'
refit(object, newy = NULL, newxreg = NULL,
  backcast.value = NULL, reestimate = FALSE, ...)

Arguments

`object`	an object of class `garchx`
`newy`	vector, the new 'y' data, see `garchx`
`newxreg`	the new 'xreg' data, if any, see `garchx`
`backcast.value`	`NULL` or a non-negative numeric, see `garchx`
`reestimate`	logical. If `FALSE` (default), then the estimates from `object` are used on the new data. If `TRUE`, then the model is re-estimated using the new data
`...`	further arguments passed to or from other methods

Details

refit.garchx is a convenience function to facilitate cross-validation and related analyses.

Value

A list of class 'garchx'

Author(s)

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

Examples

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)

##new data (e.g. 'out-of-sample' or 'test' data):
yy <- garchxSim(100)

##apply the estimates of 'mymod' on yy data:
refit(mymod, newy=yy)

##simulate from a garch(1,1):
set.seed(123)
y <- garchxSim(1000)

##estimate garch(1,1) model:
mymod <- garchx(y)

##new data (e.g. 'out-of-sample' or 'test' data):
yy <- garchxSim(100)

##apply the estimates of 'mymod' on yy data:
refit(mymod, newy=yy)

Random number generation from the multivariate normal distribution

Description

This function is a speed-optimised version of the rmnorm function from the mnormt package of Adelchi Azzalini (2013).

Usage

rmnorm(n, mean = NULL, vcov = 1)rmnorm(n, mean = NULL, vcov = 1)

Arguments

`n`	integer, the number of observations to generate
`mean`	numeric vector, i.e. the mean values
`vcov`	numeric matrix, i.e. the variance-covariance matrix

Value

A matrix of n rows

Author(s)

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

References

Adelchi Azzalini (2013): 'mnormt: The multivariate normal and t distributions', R package version 1.4-7, https://CRAN.R-project.org/package=mnormt

Examples

##generate from univariate standardised normal:
z1 <- rmnorm(100)

##generate from bivariate, independent standardised normal:
z2 <- rmnorm(100, vcov=diag(c(1,1)))

##generate from bivariate, dependent standardised normal:
z3 <- rmnorm(100, vcov=cbind(c(1,0.3),c(0.3,1)))
##generate from univariate standardised normal:
z1 <- rmnorm(100)

##generate from bivariate, independent standardised normal:
z2 <- rmnorm(100, vcov=diag(c(1,1)))

##generate from bivariate, dependent standardised normal:
z3 <- rmnorm(100, vcov=cbind(c(1,0.3),c(0.3,1)))

T-tests and Wald-tests under nullity

Description

The permissible parameter-space of GARCH-models is bounded from below by 0. This means non-standard inference is required when one or more parameters are 0 under the null hypothesis, a frequent situation in empirical applications. The functions ttest0 and waldtest0 perform t-tests and Wald-tests when one or more parameters is 0. In the latter test, the Wald-test, the critical values are obtained by simulation, see Francq and Thieu (2018).

Usage

  ttest0(x, k = NULL)
  waldtest0(x, r = 0, R = NULL, level = c(0.1,0.05,0.01),
    vcov.type = NULL, quantile.type = 7, n = 20000)
ttest0(x, k = NULL)
  waldtest0(x, r = 0, R = NULL, level = c(0.1,0.05,0.01),
    vcov.type = NULL, quantile.type = 7, n = 20000)

Arguments

`x`	an object of class 'garchx'
`k`	`NULL` (default) or a vector of integers with the coefficients to test. If `NULL`, then all coefficients apart from the intercepts are tested
`r`	`vector` with restrictions
`R`	`NULL` (default) or a full-rank `matrix`. If `NULL`, then `R` is specified such that a test of all coefficients - apart from the intercept - is equal to the restriction `r`. If `length(r)==1`, then it is recycled so that its dimension match that of `R`
`level`	`vector` of significance levels whose critical values should be computed
`vcov.type`	`NULL` or a `character` that determines the type of coefficient-covariance to use, see `vcov.garchx`
`quantile.type`	integer, the algorithm used to compute the quantile, see `quantile`
`n`	`integer`, the numer of simulations used to estimate the critical values

Details

The ttest0 function performs a t-test of coefficient k with 0 as null. Under this null the parameter is on the boundary of the admissible parameter space, and so the distribution is non-standard under the null. The function ttest0 returns the result(s) of these non-standard t-test(s), see Francq and Thieu (2018). If k=NULL, the default, then a test for each coefficient apart from the intercept is undertaken.

The waldtest0 function performs a Wald-test of the restrictions in r, when one or more of its elements are 0, see Francq and Thieu (2018).

Value

`ttest0:`	a `matrix` with the t-tests
`waldtest0:`	a `list` with the test-statistic and the critical values

Author(s)

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

References

Christian Francq and Le Quien Thieu (2018): 'QML inference for volatility models with covariates', Econometric Theory, doi:10.1017/S0266466617000512

Examples

##simulate and estimate a garch(1,1):
set.seed(123)
y <- garchxSim(1000)
mymod <- garchx(y)

##t-tests:
ttest0(mymod)

##wald-test:
waldtest0(mymod)
##simulate and estimate a garch(1,1):
set.seed(123)
y <- garchxSim(1000)
mymod <- garchx(y)

##t-tests:
ttest0(mymod)

##wald-test:
waldtest0(mymod)

Package 'garchx'

Help Index

Flexible and Robust GARCH-X Modelling

Description

Details

Author(s)

See Also

Examples

Extraction functions for 'garchx' objects

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Estimate a GARCH-X model

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Asymptotic Coefficient Covariance

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Auxiliary functions

Description

Usage

Arguments

Value

Author(s)

See Also

Simulate from a GARCH-X model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Difference a vector or a matrix, with special treatment of zoo objects

Description

Usage

Arguments

Value

Note

Author(s)

See Also

Examples

Lag a vector or a matrix, with special treatment of zoo objects

Description

Usage

Arguments

Value

Note

Author(s)

See Also

Examples

Refit a model to new data

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Random number generation from the multivariate normal distribution

Description

Usage

Lag a vector or a matrix, with special treatment of `zoo` objects