سازه های فضایی و زمانی چهار بازار مالی در چین بزرگ

We investigate the spatial and temporal structures of four financial markets in Greater China. In particular, we uncover different characteristics of the four markets by analyzing the sector and subsector structures which are detected through the random matrix theory. Meanwhile, we observe that the Taiwan and Hongkong stock markets show a negative return-volatility correlation, i.e., the so-called leverage effect. The Shanghai and Shenzhen stock markets are more complicated. Before the year 2000, the two markets exhibit a strong positive return-volatility correlation, which is called the anti-leverage effect. After 2000, however, it gradually changes to the leverage effect. We also find that the recurrence interval distributions of both the trading volume volatilities and price volatilities follow a power law behavior, while the exponents vary among different markets.

Financial markets are complex systems with many-body interactions. In recent years, much attention of physicists has been paid to the financial dynamics, and physical concepts and methods are applied to analyze the dynamic behavior. As large amounts of financial data are available now, it allows to explore the fine structure of the financial dynamics and achieve various empirical results [1], [2], [3], [4], [5], [6], [7] and [8]. With rapid development of the economy, the financial markets in Greater China attract more attention from the world. Let us now focus on four stock markets, i.e., the Shanghai stock market, Shenzhen stock market, Taiwan stock market and Hongkong stock market. Due to different political and economic systems, the dynamic behavior varies much among the four markets. The economy style of Taiwan is a typical export-oriented one. The stock market developed much through several important economic policies, such as import substitution, export expansion and structural adjustment. Hongkong is a financial center in Asia, and the economy is prosperous. The Shanghai and Shenzhen stock markets are both in mainland China, and undergoing a rapid development in recent years. To the best of our knowledge, there have not been literatures focusing on the comparative study of the spatial and temporal structures of the four stock markets, although some relevant works could be found such as the comparison between the response dynamics in transition economies and developed countries [9]. In this paper, we intend to provide a comparative study about the four stock markets, and understand how political and economic environments may influence the financial dynamics. In the past years the properties of the cross-correlation matrix of individual stock prices have been analyzed, e.g., with the random matrix theory (RMT), and much effort has been made to identify the business sectors by the components in the eigenvectors of the cross-correlation matrix [10], [11], [12], [13], [14], [15], [16] and [17]. In this paper, the analysis of the so-called spatial structure is just an analysis about the cross-correlations between individual stocks based on the RMT theory. After taking into account the signs of the components in an eigenvector, a sector may be further separated into two subsectors, i.e., the positive and negative subsectors [18]. A purpose of this paper is to investigate the spatial structures of the four stock markets in Greater China, and uncover characteristics of the sector and subsector structures for each market. The dynamic behavior of the stock prices has been studied for years, and various results have been obtained. For example, the probability distribution of the price return usually exhibits a power-law tail, the price volatility is long-range correlated in time, while the price return itself is short-range correlated [2], [19], [20] and [21]. To better understand the dynamic behavior of the stock prices, one may consider a higher-order time correlation, i.e., the return-volatility correlation [5], [6], [14] and [22]. A negative return-volatility correlation, which is called the leverage effect, was first discovered by Black in 1976 [23] and [24]. The leverage effect is observed in most of the stock markets in the world, while a positive return-volatility correlation, which is called the anti-leverage effect, was detected in the stock markets of mainland China [1], [4] and [6]. The leverage and anti-leverage effects are crucial for the understanding of the price dynamics [5], [6] and [22]. In this study, we analyze the return-volatility correlation function of the four corresponding stock-market indices, i.e., the Shanghai Composite Index, Shenzhen Composite Index, Taiwan Weighted Index and Hang Seng Index. The analysis of the recurrence interval may deepen the understanding of the dynamic behavior in financial markets [21] and [25]. Recently, statistical properties of the recurrence intervals of volume volatilities and price volatilities have been studied [26], [27], [28] and [29]. We present a comparative study on the recurrence interval distributions of the four stock markets. For each market, we analyze the recurrence interval distributions for both the trading volume volatilities and the price volatilities. The paper is organized as follows. In Section 2, we investigate the sector and subsector structures. In Section 3, we analyze the return-volatility correlation function and the distributions of the recurrence intervals for both volume volatilities and price volatilities. In Section 4, we present the conclusion.

In the RMT analysis, after taking into account the signs of the components in an eigenvector of the cross-correlation matrix, one detects that a sector may split into two subsectors, which are anti-correlated with each other in the corresponding eigenmode. For the four stock markets in greater China, the sector and subsector structures exhibit different characteristics. The Shanghai and Shenzhen markets are dominated by the Basic materials and Industrial goods subsectors. For the Taiwan market, the dominating subsectors are Electronic industry and Chemical industry, while those for the Hongkong market are Real estate & Finance and Service. All these results reflect the features of the regional economies. Meanwhile, we analyze the return-volatility correlation function. The Hongkong and Taiwan markets show a leverage effect. However, the Shanghai and Shenzhen markets are more complicated. The two markets exhibit a strong anti-leverage effect before 2000, while it gradually changes to the leverage effect after 2000. This is a new observation for the stock markets in mainland China, additional to the discovery of the anti-leverage effect in Ref. [22]. We also study the recurrence interval distributions, and find that the power law exponents for the volume volatilities range from 3.0 to 5.0 for the four markets, while those for the price volatilities are about 3.0.