Estimation of long memory in volatility using wavelets

In this work we focus on the application of wavelet-based methods in volatility modeling. We introduce a new, wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCH-family model capturing long-memory and asymmetry in volatility, and study 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, which improves the estimator performance, as we show in the experiment extension. Next, we study all the estimators in case of a FIEGARCH-Jump model, which brings interesting insights to their mechanism. We conclude that, after optimization of the estimation setup, the wavelet-based estimator may become an attractive robust alternative to the traditional methods.