BEKKs: BEKKs: Volatility modelling
In BEKKs: Multivariate Conditional Volatility Modelling and Forecasting

BEKKs

R Documentation

BEKKs: Volatility modelling

Description

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This package implements estimation, simulation and forecasting techniques for conditional volatility modelling using the BEKK model. We refer the reader to Fülle et al. (2024) for a package overview. The full BEKK(1,1,1) model of Engle and Kroner (1995) \mjdeqnH_t = CC' + A' r_t-1 r_t-1'A + G' H_t-1G ,H_t = CC' + A' r_t-1 r_t-1'A + G' H_t-1G , the asymmetric extensions of Kroner and Ng (1998) and Grier et. al. (2004) \mjdeqnH_t = CC' + A' r_t-1 r_t-1'A +B'\gamma_t-1 \gamma_t-1' B+G'H_t-1GH_t = CC' +A'r_t-1 r_t-1'A +B'\gamma_t-1 \gamma_t-1' B+G'H_t-1G,, with \mjdeqn\gamma_t = r_t I\left(r_t < 0 \right)\gamma_t = r_t I(r_t < 0 ) are implemented. Moreover, the diagonal BEKK, where the parameter matrices A, B and G are reduced to diagonal matrices and the scalar BEKK model of Ding and Engle (2001) \mjdeqnH_t = CC' + a r_t-1 r_t-1' + g H_t-1,H_t = CC' + a r_t-1 r_t-1' + g H_t-1, where a and g are scalar parameters and are implemented to allow faster but less flexible estimation in higher dimensions.

Details

The main functions are:

bekk_spec Specifies the model type to be estimated.
bekk_fit Estimates a BEKK(1,1,1) model of a given series and specification object bekk_spec.
simulate Simulates a BEKK(1,1,1) process using either a bekk_fit or bekk_spec object.
predict Forecasts conditional volatility using a bekk_fit object.
VaR Estimates (portfolio) Value-at-Risk using a fitted BEKK(1,1,1) model.
backtest Backtesting estimated (portfolio) value-at-risks of a fitted BEKK(1,1,1) model.
virf Calculates volatility impulse response functions for fitted symmetric BEKK(1,1,1) models.

Author(s)

Markus J. Fülle fuelle@uni-goettingen.de
Helmut Herwartz hherwartz@uni-goettingen.de
Alexander Lange alexander.lange@uni-goettingen.de
Christian M. Hafner christian.hafner@uclouvain.be

References

Engle, R. F. and K. F. Kroner (1995). Multivariate simultaneous generalized arch. Econometric Theory 11(1),122-150.

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.

Kroner, K. F. and V. K. Ng (1998). Modeling asymmetric comovements of asset returns. Review of Financial Studies 11(4), 817-44.

Ding, Zhuanxin and Engle, Robert F (2001). Large scale conditional covariance matrix modeling, estimation and testing. NYU working paper No. Fin-01-029.

Grier, K. B., Olan T. Henry, N. Olekalns, and K. Shields (2004). The asymmetric effects of uncertainty on inflation and output growth. Journal of Applied Econometrics 19(5), 551-565.

Hafner CM, Herwartz H (2006). Volatility impulse responses for multivariate GARCH models: An exchange rate illustration. Journal of International Money and Finance,25,719-740.

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