rugarch GARCH ModelsEasy to use functions for fitting selected GARCH-type models from
the widely-known rugarch package by Ghalanos (2024). These
functions are meant as an easy to use way to compare the main results from
rugarch to the newly established models in the fEGarch package
and are by no means considered to be a replacement of rugarch.
aparch_ru(
rt,
orders = c(1, 1),
cond_dist = c("norm", "std", "ged", "snorm", "sstd", "sged"),
meanspec = mean_spec(),
nonparspec = locpol_spec(),
use_nonpar = FALSE,
n_test = 0,
start_pars = NULL,
control_nonpar = list()
)gjrgarch_ru(
rt,
orders = c(1, 1),
cond_dist = c("norm", "std", "ged", "snorm", "sstd", "sged"),
meanspec = mean_spec(),
nonparspec = locpol_spec(),
use_nonpar = FALSE,
n_test = 0,
start_pars = NULL,
control_nonpar = list()
)
egarch_ru(
rt,
orders = c(1, 1),
cond_dist = c("norm", "std", "ged", "snorm", "sstd", "sged"),
meanspec = mean_spec(),
nonparspec = locpol_spec(),
use_nonpar = FALSE,
n_test = 0,
start_pars = NULL,
control_nonpar = list()
)
A list with the following named elements is returned.
pars:a named numeric vector with the parameter estimates.
se:a named numeric vector with the obtained standard errors in accordance with the parameter estimates.
vcov_mat:the variance-covariance matrix of the parameter estimates with named columns and rows.
rt:the input object rt (or at least the training data, if n_test is greater than zero); if rt was a "zoo" or "ts" object, the formatting is kept.
cmeans:the estimated conditional means; if rt was a "zoo" or "ts" object, the formatting is also applied to cmeans.
sigt:the estimated conditional standard deviations (or for use_nonpar = TRUE the estimated total
volatilities, i.e. scale function value times conditional standard deviation); if rt was a "zoo" or "ts" object, the formatting is also applied to sigt.
etat:the obtained residuals; if rt was a "zoo" or "ts" object, the formatting is also applied to etat.
orders:a two-element numeric vector stating the considered model orders.
cond_dist:a character value stating the conditional distribution considered in the model fitting.
llhood:the log-likelihood value obtained at the optimal parameter combination.
inf_criteria:a named two-element numeric vector with the corresponding AIC (first element) and BIC (second element) of the fitted model.
rugarch_model:the estimation object returned by ugarchfit() of the rugarch package (Ghalanos, 2024).
meanspec:the settings for the model in the conditional mean; is an object
of class "mean_spec" that is identical to the object passed to the input argument
meanspec.
test_obs:the observations at the end up the input rt reserved for
testing following n_test.
scale_fun:the estimated scale function values, if use_nonpar = TRUE, otherwise
NULL; formatting of rt is reused.
nonpar_model:the estimation object returned by tsmoothlm for
use_nonpar = TRUE.
the input time series to fit the model to ordered from
past to present; can also be a "zoo" class object or a
"ts" class object.
the ARCH and GARCH orders of the model as a two-element numeric vector.
a single-element character vector with the conditional distribution to consider.
an object of class "mean_spec"; indicates the specifications for the model in the conditional mean.
an object of class "locpol_spec" returned
by locpol_spec; defines the settings of the nonparametric
smoothing technique for use_nonpar = TRUE.
a logical indicating whether or not to implement a
semiparametric extension of the volatility model defined through spec;
see "Details" for more information.
a single numerical value indicating, how many observations
at the end of rt not to include in the fitting process and to
reserve for backtesting.
a named list with starting parameters.
a list containing changes to the arguments
for the hyperparameter estimation algorithm in the nonparametric
scale function estimation for
use_nonpar = TRUE; see "Details" for more information.
For most details, please see the documentation of the rugarch package
(Ghalanos, 2024).
These functions also provide an extension, so that a nonparametric,
smooth scale function in the unconditional standard deviation
can be estimated before the parametric step.
If use_nonpar = TRUE,
meanspec is omitted and before fitting a zero-mean model in the
conditional volatility following the remaining function arguments, a smooth scale function,
i.e. a function representing the unconditional standard deviation over time,
is being estimated following the specifications in nonparspec and
control_nonpar. This preliminary step stabilizes the input
series rt, as long-term changes in the unconditional variance
are being estimated and removed before the parametric step using
tsmooth. control_nonpar can be adjusted following
to make changes to the arguments of tsmooth
for short-memory specifications. These arguments specify settings
for the automated bandwidth selection algorithms implemented by this
function. By default, we use the settings
Mcf = "NP", InfR = "Nai",
bStart = 0.15, bvc = "Y", cb = 0.05, and
method = "lpr" for tsmooth.
locpol_spec passed to nonparspec handles
more direct settings of the local polynomial smoother itself. See
the documentation for these functions to get a detailed overview
of these settings. Assume \(\{r_t\}\) to be the observed series, where
\(t = 1, 2, \dots, n\),
then \(r_t^{*} = r_t - \bar{r}\), with \(\bar{r}\) being the arithmetic
mean over the observed \(r_t\), is computed and subsequently
\(y_t = \ln\left[\left(r_t^{*}\right)^2\right]\). The subtraction of
\(\bar{r}\) is necessary so that \(r_t^{*}\) are all different from zero
almost surely. Once \(y_t\) are available, its trend \(m(x_t)\),
with \(x_t\) as the rescaled time on the interval \([0, 1]\), is
being estimated using
tsmoothlm and denoted here by
\(\hat{m}(x_t)\). Then from \(\hat{\xi}_t = y_t - \hat{m}(x_t)\)
obtain \(\hat{C} = -\ln\left\{\sum_{t=1}^{n}\exp\left(\hat{\xi}_t\right)\right\}\),
and obtain the estimated scale function as
\(\hat{s}(x_t)=\exp\left[\left(\hat{\mu}(x_t) - \hat{C}\right) / 2\right]\).
The stabilized / standardized version of the series \(\left\{r_t\right\}\)
is then \(\tilde{r}_t = r_t^{*} / \hat{s}(x_t)\), to which
a purely parametric volatility model following the remaining function arguments
is then
fitted. The estimated volatility at a given time point is then
the product of the estimate of the corresponding scale function value
and of the estimated conditional standard deviation (following the parametric
model part) for that same time point. See for example Feng et al. (2022)
or Letmathe et al. (2023) for more information on the semiparametric extension
of volatility models.
Feng, Y., Gries, T., Letmathe, S., & Schulz, D. (2022). The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series. The R Journal, 14(1), 182-195. URL: https://journal.r-project.org/articles/RJ-2022-017/.
Ghalanos, A. (2024). rugarch: Univariate GARCH models. R package
version 1.5-3. DOI: 10.32614/CRAN.package.rugarch.
Letmathe, S., Beran, J., & Feng, Y. (2023). An extended exponential SEMIFAR model with application in R. Communications in Statistics - Theory and Methods, 53(22), 7914–7926. DOI: 10.1080/03610926.2023.2276049.
est <- gjrgarch_ru(SP500)
est@pars
est@se
plot(est@sigt)
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