روش تجزیه و تحلیل همبستگی برای ارزیابی نامتقارن فراکتال چندگانه متقابل و کاربرد آنها برای بازار مالی چین

We propose a new method called the multifractal asymmetric detrended cross-correlation analysis method (MF-ADCCA) to investigate the asymmetric cross-correlations in nonstationary time series that combine the multifractal detrended cross-correlation analysis (MF-DCCA) and asymmetric detrended fluctuation analysis (A-DFA). The study aims to determine whether different scaling properties of the cross-correlations are obtained if a one-time series trending is either positive or negative. We apply MF-ADCCA to analyze empirically the scaling behavior of the cross-correlations among the Chinese stock market, the RMB exchange market, and the US stock market. Empirical results indicate that the cross-correlations between the Chinese stock market and the RMB/USD exchange market are more persistent when any one of the markets is falling. On the contrary, the cross-correlations between the Chinese stock market and the RMB/EU, RMB/GBP, RMB/JPY exchange markets and the US stock market are more persistent when one of the markets is rising. Moreover, asymmetric cross-correlations between any two of the selected financial markets are multifractal.

Hedging crucially relies on the correlations between the assets hedged and the financial instruments used. The presence of asymmetric correlations can potentially cause problems with hedging effectiveness. Furthermore, standard mean–variance investment theory advises portfolio diversification, but the value of this advice may be questioned if all stocks tend to fall as the market falls [1]. Recently, several studies focus on asymmetric properties of financial markets or asset returns [2], [3] and [4]. Login and Solnik [5] find that international markets have greater correlations with the US market when the latter is going down than when going up. Ang and Chen [6] detect strong asymmetric correlation between stock portfolios and the US market. Ang and Bekaert [2] use the two-regime-switching model to determine the connection between low returns and high correlation. Longin and Solnik [5], defining a new concept termed exceedance correlation, report a large correlation between large negative returns, and zero correlation between large positive returns. Ang and Chen [6] use the exceedance correlation test to show that asymmetric correlation exists in different types of domestic portfolios. Hong and Zhou [1] propose a model-free method and confirm such asymmetry in the US stock market. Although these methods are able to detect the presence of asymmetric correlations, they also depend on assumptions, such as the use of a model or the selection of the threshold value. Therefore, the method of assessing asymmetric correlations is worth studying further. Recently, Podobnik and Stanley [7] and Zhou [8] propose the detrended cross-correlation analysis (DCCA) and multifractal DCCA (MF-DCCA) methods, respectively. MF-DCCA is used widely to detect the cross-correlation between financial markets [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] and [19]. Although several researchers [20], [21], [22], [23], [24], [25], [26], [27], [28] and [29] discuss the DCCA methodology, little attention focuses on the asymmetries of the cross-correlation. Alvarez-Ramirez, Rodriguez, and Echeverria [30] provide a new method called asymmetric detrended fluctuation analysis (A-DFA) to assess asymmetries in the scaling behavior of time series as a straightforward modification of the DFA method [31]. Cao, Cao, and Xu [32] apply A-DFA in investigating the asymmetric multifractal scaling behavior in the Chinese stock market. Although A-DFA only detects asymmetries of the time series itself, this method provides a new idea in measuring asymmetries of the cross-correlation which cannot be distinguished by MF-DCCA method proposed by Podobnik and Stanley [7] and Zhou [8]. Therefore, the first contribution of this paper is to propose a straightforward modification of MF-DCCA to detect the asymmetric cross-correlation between two nonstationary series. We combine MF-DCCA and A-DFA, and then propose the multifractal asymmetric detrended cross-correlation analysis method (MF-ADCCA). MF-ADCCA has three appealing features. First, it is model free. Unlike the test of Ang and Chen [6], ours is computed without having to specify a statistical model for the data. Second, MF-ADCCA is easy to implement. The MF-ADCCA scaling exponents are directly computed and several properties are given. Third, MF-ADCCA can also measure the multifractal characteristic of the different cross-correlations. The proposed method can be directly applied to a variety of fields to provide insights in assessing whether the asymmetric cross-correlation exists or not. The second contribution of this paper is to investigate the asymmetric cross-correlation between Chinese stock returns with the exchange rate of the Chinese Yuan (RMB) to different main foreign currencies and US stock returns. We assess the asymmetric cross-correlations between Chinese stock returns with the other financial returns in China when the Chinese market is rising and falling, and when the other financial markets are going up and down. Furthermore, the multifractal features of various asymmetric cross-correlation are also discussed. We find that the asymmetries exist in the cross-correlation of the Chinese stock market and the RMB exchange market, and the asymmetric cross-relations are multifractal. Moreover, the cross-correlations between the Chinese stock market and the RMB/USD exchange market are more persistent when any one of the markets is falling. On the contrary, the cross-correlations between the Chinese stock market and the RMB/EU, RMB/GBP, RMB/JPY exchange markets, and the US stock market are more persistent when any one of the markets is rising. In addition, the asymmetries of the cross-correlations between the Chinese stock market and the different RMB exchange markets present different persistences for large and small price fluctuations. The remainder of this paper is organized as follows. Section 2 presents the MF-ADCCA method, and discusses the properties of the scaling exponents. Section 3 presents and describes the basic statistical properties of the data. Section 4 applies the proposed method to Chinese financial markets. Section 5 concludes.

We developed an MF-DCCA extension to explore the existence of asymmetries in the cross-correlation scaling behavior of two time series. The MF-DCCA version separates the positive and negative trends too in studying the individual contributions to the overall scaling behavior. The empirical results on the Chinese financial markets indicate that the asymmetries are scale-dependent, which means that the cross-correlation scaling behavior for several scales is symmetric, but asymmetric for other time scales. The empirical results clearly indicate the existence of different cross-correlation properties when the trend of the financial market is going up or down. The existence of asymmetric cross-correlation adds new clues into the complex relationship of the two time series from real systems. This finding suggests that the mechanisms underlying two complex systems act in a different way depending on the directionality of the dynamics. For financial markets, these scaling behavior features will help reveal the financial markets risks and how to construct a better portfolio. Furthermore, the presence of asymmetric cross-correlations implies biased behavior of market agents. In turn, violation of the efficient market hypothesis (EMH) might be also implied. In addition, by means of this approach, our empirical study of the Chinese financial markets presents the following results. (1) Asymmetries exist in the cross-correlation of the Chinese stock market and the RMB exchange markets (except the cross-correlation between the Chinese stock market and the RMB/HK exchange market when the RMB/UK exchange market has different trends), and the asymmetric cross-correlations are multifractal. These findings might imply that the Chinese stock market and the RMB exchange markets are not strongly efficient. (2) Cross-correlations between the Chinese stock market and the RMB/USD exchange market are more persistent when any one of the markets is falling than when it is rising. On the contrary, accounting for the Chinese stock market, the RMB/EU, RMB/GBP, RMB/JPY exchange markets, and the US stock market, the cross-correlations between the Chinese stock market and any one of the other markets are more persistent when any one of these financial markets is rising than when falling. However, the cross-correlation between the Chinese stock market and the RMB/HK exchange market is more persistent when the Chinese stock market is falling than when rising. (3) Asymmetries of the cross-correlations between the Chinese stock market and the RMB/USD and RMB/HK exchange markets are less persistent for large price fluctuations than for small price fluctuations. However, the asymmetries of the cross-correlations between the Chinese stock market and the RMB/EU as well as the RMB/GBP exchange markets are more persistent for large price fluctuations than for small ones. Besides, the asymmetries of the cross-correlation between the Chinese stock market and the US stock market are stronger for large price fluctuations than for small ones.