Modeling of Long Memory in Volatility Using Wavelets
|Author:||Mgr. Lucie Kraicová|
|Year:||2013 - summer|
|Leaders:|| doc. PhDr. Jozef Baruník Ph.D.
|Work type:|| Finance, Financial Markets and Banking
|Awards and prizes:||M.A. with distinction from the Dean of the Faculty of Social Sciences for an excellent state-final examination performance and for an extraordinarily good masters diploma thesis.|
|Abstract:||This thesis focuses on one of the attractive topics of current financial literature, the
application of wavelet-based methods in volatility modeling. It introduces a new,
wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCHfamily
model capturing long-memory and asymmetry in volatility, and studies its
properties. Based on an extensive Monte Carlo experiment, both the behavior of the
new estimator in various situations and its relative performance with respect to two
more traditional estimators (maximum likelihood estimator and Fourier-based
Whittle estimator) are assessed, along with practical aspects of its application.
Possible solutions are proposed for most of the issues detected, including suggestion
of a new specification of the estimator. This uses maximal overlap discrete wavelet
transform instead of the traditionally used discrete wavelet transform, which should
improve the estimator performance in all its applications, not only in the case of
FIEGARCH model estimation. The thesis concludes that, after optimization of the
estimation setup, the wavelet-based estimator may become an attractive robust
alternative to the traditional methods.