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.
Highlights
Conventional finance theory was built on pioneering studies published in the 1950s and is based on the random walk theory and the Efficient Market Hypothesis (EMH) of [1,2]
The purpose of the empirical investigation is to compare the performance of the Generalized Autoregressive Conditional Heteroscedasticity (GARCH), EGARCH, Fractionally Integrated Generalized Autoregressive Conditional Heteroscedasticity model (FIGARCH), MRS-GARCH and Multifractal Model of Asset Returns (MMAR) and to determine which model best fits the data in the modeling of stock market index returns
Our empirical analysis consists of two parts: in the first section, we conducted the parameter estimations of the GARCH, EGARCH, FIGARCH, MRS-GARCH and MMAR models
Summary
Conventional finance theory was built on pioneering studies published in the 1950s and is based on the random walk theory and the Efficient Market Hypothesis (EMH) of [1,2]. The second important development is Drost and Werker’s [15] continuous time GARCH model that examines the statistical properties of different time scales These two developments are the basis of the Multifractal Model of Asset Returns (MMAR) introduced by Mandelbrot et al [14]. The superiority of the MMAR in the modeling is due to its incorporation of three important stylized facts of financial time series These features can be summarized as follows: first, MMAR considers fat tails of the return distributions; secondly, it has the long memory, since it uses fractal Brownian motion; and lastly, it includes the trading time property.
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