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 p^{*}, while the second element is the moving-average order q^{*}.

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 include_mean = FALSE, the unconditional mean of the series is fixed to zero and not being estimated.

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))


[Package fEGarch version 1.0.1 Index]