Iga Grzegorczyk, Katarzyna Stępień
Multiscale Multifractal Analysis (MMA) is a time series analysis method, that was first proposed by Gieraltowski et al in 2012. It is designed to describe scaling properties of fluctuations in analysed signal. As a result, it gives so called Hurst surface h(q,s), which is a dependence of the local Hurst exponent h on the multifractal parameter q and scale s, defined as data window width.
Until now the method was mainly applied in Medical Physics field e.g. to analyse time series such as heart rate variability (HRV) signals. It proved to be very effective in diagnosing patients with severe heart conditions.
The MMA method is very versatile and easily applicable. The main requirement it poses for the signal is that it has to consist of at least 15 000 samples. The other condition is that the signal cannot contain repeating fragments with high number of exactly the same values. As these are the only restrictions of the MMA method it makes it a perfect tool to analyse financial data. Some of the studies were already conducted by Pengjian Shang et al in 2014 and 2015.
Our main goal is to present the results of analysis of the financial data with the Multiscale Multifractal Analysis method and show the wide applicability MMA has in the field of economics. Although these are one of the first attempts of applying this method in such area, it allows us to draw a conclusion that MMA is suitable for analysis of financial time series, however it still requires further research.