bekk_fit: Estimating multivariate BEKK-type volatility models

In BEKKs: Multivariate Conditional Volatility Modelling and Forecasting

Estimating multivariate BEKK-type volatility models

Description

Method for fitting a variety of N-dimensional BEKK models.

Usage

bekk_fit(spec, data, QML_t_ratios = FALSE, max_iter = 50, crit = 1e-09)

Arguments

spec	An object of class "bekkSpec" from function bekk_spec.
data	A multivariate data object. Can be a numeric matrix or ts/xts/zoo object.
QML_t_ratios	Logical. If QML_t_ratios = 'TRUE', the t-ratios of the BEKK parameter matrices are exactly calculated via second order derivatives.
max_iter	Maximum number of BHHH algorithm iterations.
crit	Determines the precision of the BHHH algorithm.

Details

The BEKK optimization routine is based on the Berndt–Hall–Hall–Hausman (BHHH) algorithm and is inspired by the study of Hafner and Herwartz (2008). The authors provide analytical formulas for the score and Hessian of several MGARCH models in a QML framework and show that analytical derivations significantly outperform numerical methods.

Value

Returns a S3 class "bekkFit" object containing the estimated parameters, t-values, standard errors and volatility process of the model defined by the BEKK_spec object.

References

Hafner and Herwartz (2008). Analytical quasi maximum likelihood inference in multivariate volatility models. Metrika, 67, 219-239.

Fülle, M. J., A. Lange, C. M. Hafner, and H. Herwartz (2024). BEKKs: An R package for estimation of conditional volatility of multivariate time series. Journal of Statistical Software 111 (4), 1–34. <doi:10.18637/jss.v111.i04>.

Examples

data(StocksBonds)

# Fitting a symmetric BEKK model
obj_spec <- bekk_spec()
x1 <- bekk_fit(obj_spec, StocksBonds, QML_t_ratios = FALSE, max_iter = 50, crit = 1e-9)

summary(x1)

plot(x1)

# Fitting an asymmetric BEKK model
obj_spec <- bekk_spec(model = list(type = "bekk", asymmetric = TRUE))
x1 <- bekk_fit(obj_spec, StocksBonds)

summary(x1)

plot(x1)

# Fitting a symmetric diagonal BEKK model
obj_spec <- bekk_spec(model = list(type = "dbekk", asymmetric = FALSE))
x1 <- bekk_fit(obj_spec, StocksBonds, QML_t_ratios = FALSE, max_iter = 50, crit = 1e-9)

summary(x1)

plot(x1)


# Fitting a symmetric scalar BEKK model
obj_spec <- bekk_spec(model = list(type = "sbekk", asymmetric = FALSE))
x1 <- bekk_fit(obj_spec, StocksBonds, QML_t_ratios = FALSE, max_iter = 50, crit = 1e-9)

summary(x1)

plot(x1)

BEKKs documentation built on April 12, 2025, 1:17 a.m.