A Multifractal Detrended Fluctuation Analysis of Taiwan's Stock Exchange

This paper presents an empirical investigation on the multifractal characteristics of the Taiwan stock exchange by analyzing the minute-by-minute fluctuations in the TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) return signal. The generalized Hurst exponent, the Renyi exponent and the multifractal spectrum of the signal are evaluated using a multifractal detrended fluctuation analysis (MF-DFA), which is also applied in analyzing the multifractal properties of the logarithmic price increment (LPI) signals of 150 highly-capitalized Taiwanese companies. The results reveal the LPI signal of each company preserves multiscaling and multifractal phenomena. The relative contributions of the long-range temporal correlation and the non-Gaussian data fluctuations toward the multifractality of the time series are also examined. The results suggest that the non-Gaussian probability distributions exert a more dominant effect on the multifractality of TAIEX, but that long-range temporal correlations are more important for the LPI signals of share prices.