Performance of the Multifractal Model of Asset Returns (MMAR): Evidence from Emerging Stock Markets

Abstract

In this study, the performance of the Multifractal Model of Asset Returns (MMAR) was examined for stock index returns of four emerging markets. The MMAR, which takes into account stylized facts of financial time series, such as long memory, fat tails and trading time, was developed as an alternative to the ARCH family models. Empirical analysis of the study consists of two sections. In the first section, we estimated the parameters of GARCH, EGARCH, FIGARCH, MRS-GARCH and MMAR for the stock index returns of Croatia, Greece, Poland and Turkey. In the second section, 1000 paths were obtained for each model using Monte Carlo simulations. We then compared the scaling function values of simulated and original time series for different q orders (1–5). According to the obtained results, the MMAR is mostly superior to other models and presents the best replica of the original time series. Another important finding is the achievement of the MRS-GARCH. We found that for lower levels of persistency (long memory) of return series, the performance of the MRS-GARCH excels, and for H = 0.5, it narrowly outperforms the MMAR.

Keywords

• MMAR
• MRS-GARCH
• long memory
• fat tails