BEKK model simulation and estimation

This module allows to simulate and estimate the BEKK(1,1) model proposed in [1].

The model assumes that demeaned returns \(u_t\) are conditionally normal:

\[u_t = e_t H_t^{1/2},\quad e_t \sim N(0,I),\]

with variance matrix evolving accrding to the following recursion:

\[H_t = CC^\prime + Au_{t-1}u_{t-1}^\prime A^\prime + BH_{t-1}B^\prime.\]

References

[1]	Robert F. Engle and Kenneth F. Kroner “Multivariate Simultaneous Generalized Arch”, Econometric Theory, Vol. 11, No. 1 (Mar., 1995), pp. 122-150, <http://www.jstor.org/stable/3532933>

Notes

Check this repo for related R library: https://github.com/vst/mgarch/

Alternative optimization library: http://www.pyopt.org/

Contents

• Parameter classes
• BEKK estimation
• BEKK results
• Data generation