mean_spec {fEGarch} | R Documentation |
Specification of Conditional Mean Models
Description
Specify the model for the conditional mean in a dual model, where the conditional mean is modelled through an ARMA or a FARIMA model and the conditional standard deviations through a GARCH-type model simultaneously.
Usage
mean_spec(orders = c(0, 0), long_memo = FALSE, include_mean = TRUE)
Arguments
orders |
a two-element numeric vector with the model
orders; the first element is the autoregressive order |
long_memo |
a logical value that indicates whether the long-memory version of the model should be considered or not. |
include_mean |
a logical value indicating whether or
not to include the constant unconditional mean in the estimation
procedure; for |
Details
Let \left\{y_t\right\}
, with t \in \mathbb{Z}
as the time index,
be a theoretical time series that follows
\beta(B)(1- B)^{D}(y_t - \mu)=\alpha(B)r_t,
where \beta(B) = 1 - \sum_{i=1}^{p^{*}}\beta_i B^{i}
and
\alpha(B) = 1 + \sum_{j=1}^{q^{*}}\alpha_j B^{j}
are the AR- and MA-polynomials
of orders p^{*}
and q^{*}
, respectively, with real coefficients
\beta_i
, i=1,\dots,p^{*}
, and \alpha_j
, j=1,\dots,q^{*}
.
B
is the backshift operator. \beta(B)
and \alpha(B)
are
commonly assumed to be without common roots and to have roots outside of
the unit circle.
Furthermore, \mu
is a real-valued coefficient representing the unconditional
mean in \left\{y_t\right\}
. D \in [0, 0.5)
is the fractional
differencing parameter. \left\{r_t\right\}
is a zero-mean (weak) white
noise process, for example a member of the GARCH-models (with mean set to zero)
presented in this package (see the
descriptions in fEGarch_spec, fiaparch, figarch, etc.).
The for D=0
, which can be achieved through long_memo = FALSE
,
the formulas above describe an autoregressive moving-average (ARMA) model.
For D \in (0, 0.5)
, they describe a fractionally integrated ARMA (FARIMA)
model.
Value
An object of class "mean_spec"
is returned.
Examples
mean_spec()
mean_spec(orders = c(1, 1))