BEKKs {BEKKs}

BEKKs: Volatility modelling

Description

This package implements estimation, simulation and forecasting techniques for conditional volatility modelling using the BEKK model. The full BEKK(1,1,1) model of Engle and Kroner (1995) \[H_t = CC' + A' r_{t-1} r_{t-1}'A + G' H_{t-1}G ,\] the asymmetric extensions of Kroner and Ng (1998) and Grier et. al. (2004) \[H_t = CC' + A' r_{t-1} r_{t-1}'A +B'\gamma_{t-1} \gamma_{t-1}' B+G'H_{t-1}G\] with \[\gamma_t = r_t I\left(r_t < 0 \right)\] 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) \[H_t = CC' + a r_{t-1} r_{t-1}' + g H_{t-1},\] 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 [e-mail]

• Helmut Herwartz [e-mail]

• Alexander Lange [e-mail]

• Christian M. Hafner [e-mail]

References

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

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.