Multivariable nonlinear analysis of foreign exchange rates
Introduction
It is widely acknowledged that the market price data, e.g., stock prices and foreign exchange rates, often exhibit very complex behavior and that it is very difficult to predict their movement accurately. In order to make a good model of such financial indices and predict their complex behavior, it is essential to find which variables affect to the price movements. In the present paper, in order to solve this issue, we analyze the dealing time intervals and the spreads, the difference of bid and ask prices, of foreign exchange rates.
In the conventional studies of predicting financial data, these variables have not been often used. The reason is that the dealing time intervals have been considered to be noisy and to wonder around daily trends of business hours (that is, they are independent of the mechanism of market). However, it is very natural to anticipate that dealers’ decisions could be reflected not only by a history of price movement itself but also the history of dealing time intervals and spreads. For example, Takayasu et al. [1] showed that dealing time intervals can be described by a nonstationary Poisson process in which an average value varies depending on last several minutes. This result suggests that it is a natural idea that dealers decide dealing timings on the basis of dealing data for the last several minutes. Thus, the variable of dealing timings is not independent of the mechanism of market, and it is very essential to introduce this variable for making a good model of its mechanism.
We also introduce a new variable, that is, a spread. In foreign exchange market, since there is the rule of “Two Way Quotation” that a bank must quote both bid and ask prices to another bank simultaneously, there exists a spread between bid and ask prices by every deal. It is very natural that these prices reflect the balance of demands and supplies, dealers’ mind and the mood of a market which influence price movements. Namely, the variable of spreads is useful to understand the mechanism of market. In addition, we see that the spread follows a power law in our previous research [2]. Stanley, et al. also showed that the price movements have a non-gaussian distribution and also follows the power law [3]. Since the spread shows a similar statistical property to the price movements, we highly expect that the spread has relation to the mechanism of market as well as dealing time intervals.
Section snippets
The data for analysis
In the present paper, we use the time series of tick data between the US dollar and the Swiss franc observed in the interbank market [4]. The tick data is recorded from January 1986 to April 1991 (total 1322 days), and the total number of the data points is 282,956. Usually, tick data has the following intrinsic aspects. There is a sort of discontinuity on dairy tick data, because the bank closes at nights, weekends and holidays. Then the first and the last dealing times are different from each
Nonlinear modeling with three variables
If there is a dynamical relationship between |ΔP|, τ and S, adopting three variables would improve prediction performance. Since the movement of spreads is much smaller than the others, we have to use a large amount of the learning data. Here, we have to treat again the issue that there is a discontinuity of dairy data. Namely, simple connection of each dairy data might lead us to spurious results, because the dealers cannot deal from closing time to opening time of the next day, and because
Conclusions
In the present paper, we show the existence of a dynamical interaction among the middle prices, the dealing time intervals and the spreads from the viewpoint of ensemble behavior in each day. We also use multivariables for a reconstructing attractor and modify the conventional local linear approximation method in order to treat discontinuity of dairy data. As a result, our scheme with multivariable reconstruction improves all signature errors and root mean square errors, which means that our
References (10)
- H. Takayasu, M. Takayasu (Eds.), Econophysics-Toward Scientific Reconstruction of Economy, Nihon Keizai Shimbun, 2001...
- T. Suzuki, T. Ikeguchi, M. Suzuki, Modeling on complex behavior of interbank exchange markets, 2003, submitted for...
- et al.
Scaling behavior in the dynamics of an economic index
Nature
(1995) - A.S. Weigend, N.A. Gershenfeld (Eds.), Time Series Prediction, Addison-Wesley, Reading, MA,...
- et al.
Design of a laboratory for multineuron studies
IEEE Trans. Syst. Man Cybern.
(1983)
Cited by (5)
A model of complex behavior of interbank exchange markets
2004, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :In the present paper, we propose a model of interbank exchange dealing by using not only price movements but also the spreads and the dealing time intervals. In our previous study [15], using real data of the interbank exchange market between the Swiss franc and the US dollar, we have already analyzed the interaction among the price movements, the dealing time intervals and the spreads of real data, and we have discovered that when the spread becomes larger, the dealing time interval becomes shorter and the movement of price becomes larger [15]. Since the expansion of the spread means that ask and bid prices are separated from the middle price, it is natural to consider that the dealer tries to sell at higher prices and to buy at lower prices.
Online apnea–bradycardia detection based on hidden semi-Markov models
2015, Medical and Biological Engineering and ComputingAppropriate time scales for nonlinear analyses of deterministic jump systems
2011, Physical Review E - Statistical, Nonlinear, and Soft Matter PhysicsMultivariate time series prediction by neural network combining SVD
2006, Conference Proceedings - IEEE International Conference on Systems, Man and CyberneticsMultivariate chaotic time series prediction based on radial basis function neural network
2006, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)