Abstract
Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in time series. In this paper, DFA is employed to discuss the long-range correlations of stock market. The effects of exponential trends on correlations of Hang Seng Index (HSI) are investigated with emphasis. We find that the long-range correlations and the positions of the crossovers of lower order DFA appear to have no immunity to the additive exponential trends. Further, our analysis suggests that an increase in the DFA order increases the efficiency of eliminating on exponential trends. In addition, the empirical study shows that the correlations and crossovers are associated with DFA order and magnitude of exponential trends.
Highlights
Financial markets have been known as representative complex dynamic systems, which are organized by various unexpected phenomena and affected by external factors
The long-range correlation behaviors in absolute log returns are investigated by applying detrended fluctuation analysis (DFA)
We find that the absolute log returns of New York Stock Exchange Composite Index (NYSE) and Hang Seng Index (HSI) are long-range correlated; the long-range correlation of NYSE is stronger than HSI
Summary
Financial markets have been known as representative complex dynamic systems, which are organized by various unexpected phenomena and affected by external factors. The bulk of the literature focused on the long-range correlations of financial time series in the past few years. New ideas and techniques have been introduced to measure the longrange correlation behaviors. Many researchers have found evidence of long-range correlations for stock markets [2–5]. To analyze the longrange correlations, previous studies presented various methods, such as rescaled range analysis (R/S analysis), wavelet transform modulus maxima (WTMM), and detrended fluctuation analysis (DFA) [6, 7]. The DFA [8] method invented by Peng et al has become a widely used method for the determination and detection of long-range correlations in time series. One reason to employ the DFA method is to avoid spurious detection of correlations that are artifacts of nonstationarities in the time series. Strong trends in series may lead to a false detection of long-range correlations. For the reliable detecting of long-range correlations, it is essential to distinguish trends from the intrinsic long-range fluctuations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
