Empirical Wavelet Analysis of Tail and Memory Properties of LARCH and FIGARCH Models

Using computationally efficient wavelet methods, we study two nonlinear models of financial returns {r t }: linear ARCH (LARCH) and fractionally integrated GARCH (FIGARCH). We estimate the tail index alfa and the long memory parameter d of the squared returns Xt=rt2 of LARCH, and of the powers X t = |r t | p of FIGARCH. We find that the X t have infinite variance and long memory, and show how the estimates of alfa and d depend on the model parameters. These relationships are determined empirically, as the setting is quite complex, and no suitable theory has been developed so far. In particular, we provide empirical relationships between the estimates d and the difference parameters in LARCH and FIGARCH. Our computational work uncovers tail and memory properties of LARCH and FIGARCH for practically relevant parameter ranges, and provides some guidance on modeling returns on speculative assets including FX rates, stocks and market indices.

Empirical Wavelet Analysis of Tail and Memory Properties of LARCH and FIGARCH Models Articles