BEKKs: An R Package for Estimation of Conditional Volatility of Multivariate Time Series

35 Pages Posted: 9 Dec 2022 Last revised: 16 Dec 2022

See all articles by Markus J. Fülle

Markus J. Fülle

University of Goettingen (Göttingen)

Alexander Lange

University of Goettingen (Göttingen)

Christian Hafner

Catholic University of Louvain (UCL) - School of Statistics; Tinbergen Institute

Helmut Herwartz

University of Goettingen (Göttingen)

Date Written: September 29, 2022

Abstract

We describe the R-Package BEKKs, which implements the estimation and diagnostic analysis of a prominent family of multivariate generalized autoregressive conditionally heteroskedastic (MGARCH) processes, the so-called BEKK models. Unlike existing software packages, we make use of analytical derivatives implemented in efficient C++ code for nonlinear log-likelihood optimization. This allows fast parameter estimation even in higher model dimensions N > 3. The baseline BEKK model is complemented with an asymmetric parametrization that allows for a flexible quadrant-specific modelling of conditional (co)variances. Furthermore, we provide the user with the simplified scalar and diagonal BEKK models to deal with high dimensionality of heteroskedastic time series. The package is designed in an object-oriented way featuring a comprehensive toolbox of methods to investigate and interpret, for instance, volatility impulse response functions, risk estimation and forecasting (VaR) and a backtesting algorithm to compare the forecasting performance of alternative BEKK models. For illustrative purposes, we analyse a bivariate ETF return series (S&P, US treasury bonds) and a four-dimensional system comprising, in addition, a gold ETF and changes of a log oil price by means of the suggested package. We find that the BEKKs package is more than 100 times faster for time series systems of dimension N>3 than other existing packages.

Keywords: BEKK Model, Multivariate GARCH, Leverage Effect, Value-At-Risk, Impulse Response Functions, R

Suggested Citation

Fülle, Markus J. and Lange, Alexander and Hafner, Christian and Herwartz, Helmut, BEKKs: An R Package for Estimation of Conditional Volatility of Multivariate Time Series (September 29, 2022). Available at SSRN: https://ssrn.com/abstract=4233296 or http://dx.doi.org/10.2139/ssrn.4233296

Markus J. Fülle (Contact Author)

University of Goettingen (Göttingen) ( email )

Platz der Gottinger Sieben 3
Gottingen, D-37073
Germany

Alexander Lange

University of Goettingen (Göttingen) ( email )

Platz der Gottinger Sieben 3
Gottingen, D-37073
Germany

Christian Hafner

Catholic University of Louvain (UCL) - School of Statistics ( email )

Voie du Roman Pay
34 B-1348 Louvain-La-Neuve, 1348
Belgium

Tinbergen Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Helmut Herwartz

University of Goettingen (Göttingen) ( email )

Platz der Gottinger Sieben 3
Gottingen, D-37073
Germany

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