شاخص گذاری نوسانات فعالیت های اخبار نقل قولی در بازار ارز

We study the scaling behavior of quotation activities for various currency pairs in the foreign exchange market. The components’ centrality is estimated from multiple time series and visualized as a currency pair network. The power-law relationship between a mean of quotation activity and its standard deviation for each currency pair is found. The scaling exponent αα and the ratio between common and specific fluctuations ηη increase with the length of the observation time window View the MathML sourceΔt. The result means that although for View the MathML sourceΔt=1(min), the market dynamics are governed by specific processes, and at a longer time scale View the MathML sourceΔt>100(min) the common information flow becomes more important. We point out that quotation activities are not independently Poissonian for View the MathML sourceΔt=1(min), and temporally or mutually correlated activities of quotations can happen even at this time scale. A stochastic model for the foreign exchange market based on a bipartite graph representation is proposed.

The complexity of economic and social systems has attracted a lot of attention from physicists recently [1], [2], [3], [4], [5], [6], [7] and [8]. Collective behavior among interacting agents shows different properties from particles governed by Newtonian laws. However, intriguing universal properties could be found and mathematical models should be considered. This movement, called socio/econo-physics, is expected to bridge a gap between physics and our societies [9]. Financial markets are complex systems which consist of many interacting agents. The progress of understanding information flows among agents sheds light on the states of financial markets, i.e. the states of market participants. The recent accumulation of a massive amount of data about financial markets due to both the development and spread of information and communication technology allows us to quantify the states of financial markets in detail [10] and [11]. In fact, the correlation structure of high-frequency financial time series is exhaustively and quantitatively investigated [12] and [13]; however, the further the dimension of multiple time series increases, the more difficult it becomes to compute cross-correlations and to recognize them. On the other hand, several studies in both socio/econo-physics and engineering were focused on the structure of corresponding complex networks, their internal dynamics and the flows of the constituents on them [14], [15], [16] and [17]. Menezes and Barabási studied the scaling behavior of constituents’ flows on several constructions such as river networks (water flows), transportation systems (car flows), and computer networks (information flows) [18] and [19]. As a result, scaling properties are found for flow fluctuations in such systems. This relationship is known as a fluctuation scaling or Taylor’s power law [20] and [21]. Taylor’s power law is known as the scaling relationship between the mean of populations and their standard deviation in ecological systems. The ubiquity of Taylor’s power-law slopes between 1/2 and 1 suggests that there exists an underlying fundamental mechanism affecting the transportation of constituents. Eisler and Kertész found that there is such a power-law relationship between a mean of traded volumes of stocks and their standard deviation on the New York Stock Exchange, and that the power-law exponent takes nontrivial values between 1/2 and 1 [22]. Jian et al. investigated trade volumes of stocks in the Chinese stock market [23]. They also found a non-universal scaling exponent of different fluctuations from 1/2 and 1. We think that their results provide a method to quantify the states of agents with multiple time series in the financial markets. This method is also useful to quantify the states of market participants from the viewpoint of information flows in financial markets. The aim of this paper is to investigate information flows in the foreign exchange market (FX market) by means of quotation activities, measured as arrival rates of quotations on brokerage systems. We investigate the statistical properties of quotation activities in the FX market and quantify the total states of the market participants through fluctuation scaling. The organization of this paper is as follows. Section 2 is a short overview of high-frequency financial data taken for our studies from the FX market. Section 3 is a brief summary of the power-law relationship (Taylor scaling) between a mean of constituents’ flow on a graph and their standard deviations. In Section 4 an empirical analysis of quotation activities is performed. In Section 5 the dependence of scaling exponents on a time window length is examined, and the relationship between the states of market participants in the FX market and the scaling exponents is discussed. Section 6 is devoted to concluding remarks, and addresses possible future studies.

We found the power-law relationship between means of quotation activities for currency pairs at the FX and their standard deviation. The scaling exponents αα take values in a range from 0.8 to 0.9; they increase with the time window View the MathML sourceΔt and vary in time depending on observation days. The nontrivial value of αα implies that market participants may be affected by both endogenous and exogenous factors, or that they behave with a strong temporal correlation. The dependence αα can be explained by the heterogeneity of Hurst exponents that increase with the mean activity of a given currency pair. This dependence also follows from the increasing contribution of common fluctuations for larger View the MathML sourceΔt and can be related to synchronous and desynchronous states of information transmission in the FX market. The standard deviations of the specific fluctuations scale with αspe≈0.68αspe≈0.68 as a function of activity means and this scaling exponent is nearly independent of the time window View the MathML sourceΔt. The specific fluctuations dominate the dynamics of rare currency pairs, while the common fluctuations are essential for hard currency pairs with large mean activity. It follows from our analysis that for short time scale View the MathML sourceΔt≈1(min), the dynamics of the FX market are substantially driven by the specific processes while for View the MathML sourceΔt around 2 (h) the common factors start to be important. This observation is consistent with the results of [27] on the stock market fluctuations. It means that in the stock markets and in the FX market, incoming news shows finite time diffusion on the short time scale. On the other hand, since the coherent response can be observed, collective decisions occur at a longer time scale. There are certain similarities as well as differences between our results for FX market quotation activity fluctuations and observations of the stock market value fluctuations [22] and [27]. In both cases there is a Taylor-like scaling of fluctuation amplitudes with nonuniversal characteristic exponents αα dependent on the time window View the MathML sourceΔt. Hurst exponents for both systems increase with mean activity View the MathML source〈Xi,Δt〉 of a currency pair or of a mean stock value. This dependence is, however, very clear for the stock market data (in the case of View the MathML sourceΔ>300(min) and it is very noisy for the FX market. The other important difference is the magnitude of common fluctuations View the MathML sourceσi,Δtcom that, in the case of the FX market can be larger than the amplitude of specific fluctuations View the MathML sourceσi,Δtspe even for short time scales View the MathML sourceΔt=1(min) for very active currency pairs with large centrality values (e.g. GBP/CHF or GBP/JPY). As for future work, more careful analysis, including the relationship between auto-correlation and cross-correlation, is needed. In addition, persistent investigation using exhaustive data for long periods, and mathematical modeling of the FX market from an information transmission point of view, should be conducted. One candidate for an adequate model is that of the stochastic processes [18] and [20] and another is that of agent-based models in the financial markets [8], [33] and [34].