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Investigating efficiency of frontier stock markets using multifractal detrended fluctuation analysis

Faheem Aslam (COMSATS University Islamabad, Islamabad, Pakistan)
Paulo Ferreira (VALORIZA - Research Center for Endogenous Resource Valorization, Portalegre, Portugal) (Instituto Politécnico de Portalegre, Portalegre, Portugal) (CEFAGE-UE, IIFA, Universidade de Évora, Évora, Portugal)
Wahbeeah Mohti (Department of Business Administration, Iqra University – Islamabad Campus, Islamabad, Pakistan)

International Journal of Emerging Markets

ISSN: 1746-8809

Article publication date: 30 June 2021




The investigation of the fractal nature of financial data has been growing in the literature. The purpose is to investigate the multifractal behavior of frontier markets using multifractal detrended fluctuation analysis (MFDFA).


This study used daily closing prices of nine frontier stock markets up to 31-Aug-2020. A preliminary analysis reveals that these markets exhibit fat tails and clustering patterns. For a more robust analysis, a combination of Seasonal and Trend Decomposition using Loess (STL) and MFDFA has been employed. The former method is used to decompose daily stock returns, where later detected the long rang dependence in the series.


The results confirm varying degree of multifractality in frontier stock markets, implying that they exhibit long-range dependence. Based on these multifractality levels, Serbian and Romanian stock markets are the ones exhibiting least long-range dependence, while Slovenian and Mauritius stock markets indicating highest dependence in their series. Furthermore, the markets of Kenya, Morocco, Romania and Serbia exhibit mean reversion (anti-persistent) behavior while the remaining frontier markets show persistent behaviors.

Practical implications

The information given by the detection of the fractal measure of data can support for investment and policymaking decisions.


Frontier markets are of great potential from the perspective of international diversification. However, most of the research focused on other emerging and developed markets, especially in the context of multifractal analysis. This study combines the STL method and a physics-based robust technique, MFDFA to detect the multifractal behavior of frontier stock markets.



Paulo Ferreira acknowledges the financial support of Fundação para a Ciência e a Tecnologia (grants UIDB/05064/2020 and UIDB/04007/2020).


Aslam, F., Ferreira, P. and Mohti, W. (2021), "Investigating efficiency of frontier stock markets using multifractal detrended fluctuation analysis", International Journal of Emerging Markets, Vol. ahead-of-print No. ahead-of-print.



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