رفتار نامتقارن چند فراکتالی تجانسی در بازار بورس چینی: بر اساسMF-DFAنامتقارن

We utilized asymmetric multifractal detrended fluctuation analysis in this study to examine the asymmetric multifractal scaling behavior of Chinese stock markets with uptrends or downtrends. Results show that the multifractality degree of Chinese stock markets with uptrends is stronger than that of Chinese stock markets with downtrends. Correlation asymmetries are more evident in large fluctuations than in small fluctuations. By discussing the source of asymmetric multifractality, we find that multifractality is related to long-range correlations when the market is going up, whereas it is related to fat-tailed distribution when the market is going down. The main source of asymmetric scaling behavior in the Shanghai stock market are long-range correlations, whereas that in the Shenzhen stock market is fat-tailed distribution. An analysis of the time-varying feature of scaling asymmetries shows that the evolution trends of these scaling asymmetries are similar in the two Chinese stock markets. Major financial and economical events may enhance scaling asymmetries.

The presence of multifractality suggests the inefficiency [1], [2], [3], [4], [5] and [6], volatility predictability [7], crash predictions [8] and [9], and complexity [10], [11] and [12] of the market. Multifractal analysis has been widely applied in stock markets [13] and [14] to investigate the intermittent nature of turbulence. Multifractal detrended fluctuation analysis (MF-DFA) [15], which is based on detrended fluctuation analysis (DFA) [16], is widely used to detect long-range autocorrelations and multifractality in stock markets for nonstationary time series [17] and [18]. Numerous studies have analyzed multifractality in the Chinese stock market [19], [20], [21], [22], [23], [24] and [25], but relatively few have focused on the asymmetry of multifractal scaling behavior. Even though a small number of studies [26] have focused on this field, researchers usually investigate the different correlation features by categorizing the period of stock markets into bull and bear, in which the sample division is subjective. Thus, studying asymmetric correlation in the entire sample interval is necessary. This study intends to fill this research gap. Correlation asymmetry affects portfolio diversification, risk management, and policymaking [27]. The presence of asymmetric correlation in the stock market is not surprising because of the expected asymmetric response to economic news. Recent studies suggest that asymmetric correlations exist in stock returns [28], [29] and [30]. Ang and Bekaert [31] utilized a two-regime-switching model to determine the connection between low returns and high correlation. Longin and Solnik [28] define a new concept called “exceedance correlation” and find a high correlation between large negative returns and zero correlation between large positive returns. Ang and Chen [29] use an exceedance correlation test and show that an asymmetric correlation exists in different types of domestic portfolios. Hong and Zhou [32] propose a model-free method and confirm that asymmetry exists in the United States stock market. These methods can detect the presence of asymmetric correlations. However, these methods depend on assumptions, such as model and threshold value selection. Alvarez-Ramirez et al. [33] extended the DFA in 2009 by developing asymmetric DFA (A-DFA) method to explore the asymmetries in the scaling behavior of time series. We call the A-DFA method “A-MFDFA” in this paper because A-DFA can analyze multifractal scaling behavior. The A-MFDFA method can not only assess multifractality in different correlations but can also detect the asymmetry of scaling behavior in time series with uptrends and downtrends. Alvarez-Ramirez et al. show that different scaling properties exist if the signal trend is positive or negative. However, Alvarez-Ramirez et al. only show intuitively the relationship between asymmetric behavior and intrinsic correlations. They also discuss only the skewness of data distribution in their samples rather than the origins of asymmetric behavior. Our work aims to achieve three objectives. First, we apply A-MFDFA to explore the existence of asymmetric multifractal scaling behavior in the Shanghai and Shenzhen stock markets. Second, we discuss the source of asymmetric multifractal scaling behavior by comparing the estimated results of the original data with those of shuffled and surrogated data. Third, we apply rolling windows method to investigate the time-varying feature of scaling asymmetries in the Chinese stock market. The results show that the degree of multifractality in the Chinese stock market with uptrends is stronger than that in the Chinese stock market with downtrends. Correlation asymmetries are stronger in large fluctuations than in small fluctuations. Long-range correlations are the main source of multifractality when the market has uptrends, whereas fat-tailed distribution is the main source of multifractality when the market has downtrends. In particular, the main source of multifractal scaling behavior in the Shanghai stock market is fat-tailed distribution, whereas that in the Shanghai stock market are long-range correlations. The multifractality in the Shenzhen stock market is induced by long-range correlations, whereas that in the Shenzhen stock market is related to fat-tailed distribution. The evolution of scaling asymmetries is similar in the two Chinese stock markets. Major financial and economic events may enhance these asymmetries. The rest of the paper is organized as follows. Section 2 introduces the A-MFDFA method. Section 3 presents the basic statistical properties of the data. Section 4 provides an empirical analysis of the proposed method, and Section 5 concludes the paper.

We first applied A-MFDFA method in this paper to investigate asymmetric multifractal scaling behavior in the Shanghai and Shenzhen stock markets in China. The sources of multifractality and asymmetry for these two markets are studied. Results show that the price memory in the Chinese stock market is longer when the market is going down than when it is going up. This finding may be different from that of Zhou et al. [26], who suggest that the bull market shows stronger long-term correlation than the bear market. However, we obtain the same result as Bai and Zhu [55], who suggest that the correlation of the Shenzhen stock market is stronger than that of the Shanghai stock market. The following is a summary of our results: (i) The Chinese stock market demonstrates multifractal scaling behavior, but the multifractality degree for uptrends is stronger than that for downtrends. The correlation asymmetries are stronger for large fluctuations than for small fluctuations. (ii) Either long-range correlation or fat-tailed distribution induces scaling multifractality in the Chinese stock market. However, the main source of multifractal scaling behavior is more related to long-range correlation when the market is going up, whereas the main source of multifractal scaling behavior is more related to fat-tailed distribution when the market is going down. (iii) The main sources of scaling multifractality and scaling asymmetry in the Shanghai stock market are related to fat-tailed distribution and long-range correlations, respectively. The scaling multifractality and scaling asymmetry in the Shenzhen stock market are induced by long-range correlation and fat-tailed distribution, respectively. (iv) The scaling asymmetries in SSCI and SZCI possess time-varying features, and the trends of evolution of these scaling asymmetries are almost similar. The scaling asymmetry in the Chinese stock market (both for SSCI and for SZCI) may increase significantly because of dramatic changes in the external economic and financial environment, such as financial crises, reforms in the stock market, and QFII. This paper studies the nonlinear mechanism of the stock market from a new perspective. The presence of scaling asymmetry suggests that the mechanisms underlying a complex system act in a different way on the basis of the direction of the dynamics [33]. However, additional studies are needed to confirm or improve the conclusions in our paper. Refs. [56] and [57] show that a finite-size effect in our empirical analysis may be present, and additional data are needed to obtain reliable results because a window length of 5000, which is the length of the time series in our study, is not short. However, this duration is not long enough to eliminate the finite-size effect. Moreover, the asymmetric MF-DCCA method can be proposed in further research as an extension of the detrended cross-correlations method [46], [58], [59], [60] and [61] to study the relationship of multifractality and long-range cross-correlations when the market is going up and down.