This article proposed a hybrid detrended deconvolution foreign exchange network construction method (DDFEN), which combined the detrended cross-correlation analysis coefficient (DCCC) and the network deconvolution method together. DDFEN is designed to reveal the `true' correlation of currencies by filtering indirect effects in the foreign exchange networks (FXNs). The empirical results show that DDFEN can reflect the change of currency status in the long term and also perform more stable than traditional network construction methods.
We analyze structure of the world foreign currency exchange (FX) market viewed as a network of interacting currencies. We analyze daily time series of FX data for a set of 63 currencies, including gold, silver and platinum. We group together all the exchange rates with a common base currency and study each group separately. By applying the methods of filtered correlation matrix we identify clusters of closely related currencies. The clusters are formed typically according to the economical and geographical factors. We also study topology of weighted minimal spanning trees for different network…
This study investigates that a characteristic time scale on an exchange rate market (USD/JPY) is examined for the period of 1998 to 2000. Calculating power spectrum densities for the number of tick quotes per minute and averaging them over the year yield that the mean power spectrum density has a peak at high frequencies. Consequently it means that there exist the characteristic scales which dealers act in the market. A simple agent model to explain this phenomenon is proposed. This phenomena may be a result of stochastic resonance with exogenous periodic information and physiological fluctuat…
The currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the markets have rational risk-neutral investors, then one would not expect profits from such strategies. That is uncovered interest rate parity (UIP), the parity condition in which exposure to foreign exchange risk, with unanticipated changes in exchange rates, should result in an o…
In a system containing a large number of interacting stochastic processes, there will typically be many non-zero correlation coefficients. This makes it difficult to either visualize the system's inter-dependencies, or identify its dominant elements. Such a situation arises in Foreign Exchange (FX) which is the world's biggest market. Here we develop a network analysis of these correlations using Minimum Spanning Trees (MSTs). We show that not only do the MSTs provide a meaningful representation of the global FX dynamics, but they also enable one to determine momentarily dominant and dependent…
We investigate topology and temporal evolution of the foreign currency exchange market viewed from a weighted network perspective. Based on exchange rates for a set of 46 currencies (including precious metals), we construct different representations of the FX network depending on a choice of the base currency. Our results show that the network structure is not stable in time, but there are main clusters of currencies, which persist for a long period of time despite the fact that their size and content are variable. We find a long-term trend in the network's evolution which affects the USD and …
Econophysics is a science in its infancy, born about ten years ago at this time of writing, at the crossing roads of physics, mathematics, computing and of course economics and finance. It also covers human sciences, because all economics is ultimately driven by human decision. From this human factor, econophysics has no hope to achieve the status of an exact science, but it is interesting to discover what can be achieved, discovering potential limits and trying try to push further away these limits. A few data analysis techniques are described with emphasis on the Detrended Fluctuation Analys…
We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming that stochastic processes of the market price changes could be regarded as a renewal process, we use the theorem to calculate the average waiting time of the process. In the conventional derivation of the theorem, it is apparently hard to evaluate the higher order moments of the wa…
We propose a useful approach for investigating the statistical properties of foreign currency exchange rates. Our approach is based on queueing theory, particularly, the so-called renewal-reward theorem. For the first passage processes of the Sony Bank US dollar/Japanese yen (USD/JPY) exchange rate, we evaluate the average waiting time which is defined as the average time that customers have to wait between any instant when they want to observe the rate (e.g. when they log in to their computer systems) and the next rate change. We find that the assumption of exponential distribution for the fi…
We investigate quotation and transaction activities in the foreign exchange market for every week during the period of June 2007 to December 2010. A scaling relationship between the mean values of number of quotations (or number of transactions) for various currency pairs and the corresponding standard deviations holds for a majority of the weeks. However, the scaling breaks in some time intervals, which is related to the emergence of market shocks. There is a monotonous relationship between values of scaling indices and global averages of currency pair cross-correlations when both quantities …
High-frequency financial data of the foreign exchange market (EUR/CHF, EUR/GBP, EUR/JPY, EUR/NOK, EUR/SEK, EUR/USD, NZD/USD, USD/CAD, USD/CHF, USD/JPY, USD/NOK, and USD/SEK) are analyzed by utilizing the Kullback-Leibler divergence between two normalized spectrograms of the tick frequency and the generalized Jensen-Shannon divergence among them. The temporal structure variations of the similarity between currency pairs is detected and characterized. A simple agent-based model in which $N$ market participants exchange $M$ currency pairs is proposed. The equation for the tick frequency is approx…
We investigate the relative market efficiency in financial market data, using the approximate entropy(ApEn) method for a quantification of randomness in time series. We used the global foreign exchange market indices for 17 countries during two periods from 1984 to 1998 and from 1999 to 2004 in order to study the efficiency of various foreign exchange markets around the market crisis. We found that on average, the ApEn values for European and North American foreign exchange markets are larger than those for African and Asian ones except Japan. We also found that the ApEn for Asian markets incr…
For the purpose of elucidating the correlation among currencies, we analyze daily and high-resolution data of foreign exchange rates. There is strong correlation for pairs of currencies of geographically near countries. We show that there is a time delay of order less than a minute between two currency markets having a strong cross-correlation. The cross-correlation between exchange rates is lower in shorter time scale in any case. As a corollary we notice a kind of contradiction that the direct Yen-Dollar rate significantly differs from the indirect Yen-Dollar rate through Euro in short time …
We develop the optimal trading strategy for a foreign exchange (FX) broker who must liquidate a large position in an illiquid currency pair. To maximize revenues, the broker considers trading in a currency triplet which consists of the illiquid pair and two other liquid currency pairs. The liquid pairs in the triplet are chosen so that one of the pairs is redundant. The broker is risk-neutral and accounts for model ambiguity in the FX rates to make her strategy robust to model misspecification. When the broker is ambiguity neutral (averse) the trading strategy in each pair is independent (depe…
World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rates within the basket of 60 currencies in the period December 1998 -- May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the persp…
We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar from 1991 to 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and after the crisis. We find that the Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to Hong-Kong and Japan. We also show that the multifractality is stronge rel…
There are many studies dealing with the analysis of similarity among currencies in foreign exchange market by using network analysis approach. In those studies, each currency is represented by a univariate time series of exchange rate return. This is the standard practice to analyze the underlying information in the foreign exchange market. In this paper, Escoufier's RV coefficient is applied to measure the similarity among currencies where each of them is represented by bivariate time series. Based on that coefficient, we analyze the topological structure of the currencies. An example of FORE…
Copulas are used to construct joint distributions in many areas. In some problems, it is necessary to deal with correlation structures that are more complicated than the commonly known copulas. A finite order multivariate Hermite polynomial expansion, as an approximation of a joint density function, can handle complex correlation structures. However, it does not construct copulas because the density function can take negative values. In this study, we propose a method to construct a copula based on the finite sum of multivariate Hermite polynomial expansions by applying corrections to the join…
There is intense interest in understanding the stochastic and dynamical properties of the global Foreign Exchange (FX) market, whose daily transactions exceed one trillion US dollars. This is a formidable task since the FX market is characterized by a web of fluctuating exchange rates, with subtle inter-dependencies which may change in time. In practice, traders talk of particular currencies being 'in play' during a particular period of time -- yet there is no established machinery for detecting such important information. Here we apply the construction of Minimum Spanning Trees (MSTs) to the …
This study considers the multivariate segmentation procedure under the assumption of the multivariate Gaussian mixture. Jensen-Shannon divergence between two multivariate Gaussian distributions is employed as a discriminator and a recursive segmentation procedure is proposed. The daily log-return time series for 30 currency pairs consisting of 12 currencies for the last decade (January 3, 2001 to December 30, 2011) are analyzed using the proposed method. The proposed method can detect several important periods related to the significant affairs of the international economy.
The foreign exchange market has taken an important role in the global financial market. While foreign exchange trading brings high-yield opportunities to investors, it also brings certain risks. Since the establishment of the foreign exchange market in the 20th century, foreign exchange rate forecasting has become a hot issue studied by scholars from all over the world. Due to the complexity and number of factors affecting the foreign exchange market, technical analysis cannot respond to administrative intervention or unexpected events. Our team chose several pairs of foreign currency historic…
Contagion is an extremely important topic in finance. Contagion is at the core of most major financial crises, in particular the 2008 financial crisis. Although various approaches to quantifying contagion have been proposed, many of them lack a causal interpretation. We will present a new measure for contagion among individual currencies within the Foreign exchange market and show how the paths of contagion work within the Forex using causal inference. This approach will allow us to pinpoint sources of contagion and to find which currencies offer good options for diversification and which are …
Correlation matrices of foreign exchange rate time series are investigated for 60 world currencies. Minimal Spanning Tree (MST) graphs for the gold, silver and platinum are presented. Inverse power like scaling is discussed for these graphs as well as for four distinct currency groups (major, liquid, less liquid and non-tradable). The worst scaling has been found for USD and related currencies.
The Euro (EUR) has been a currency introduced by the European Community on Jan. 01, 1999. This implies eleven countries of the European Union which have been found to meet the five requirements of the Maastricht convergence criteria. In order to test EUR behavior and understand various features, we have extrapolated the EUR backwards and therefore have obtained a {\it false euro} (FEUR) dating back to 1993. We have derived the exchange rates of the FEUR with respect to several currencies of interest not belonging to the EUR, i.e., Danish Kroner (DKK), Swiss Franc (CHF), Japanese Yen (JPY) and …
By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countries in the world such as Asia or East Europe, the key currencies are generally given by major economic countries as expected.
We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Tem…
Reinforcement learning can interact with the environment and is suitable for applications in decision control systems. Therefore, we used the reinforcement learning method to establish a foreign exchange transaction, avoiding the long-standing problem of unstable trends in deep learning predictions. In the system design, we optimized the Sure-Fire statistical arbitrage policy, set three different actions, encoded the continuous price over a period of time into a heat-map view of the Gramian Angular Field (GAF) and compared the Deep Q Learning (DQN) and Proximal Policy Optimization (PPO) algori…
This paper reports empirical evidence that a neural networks model is applicable to the statistically reliable prediction of foreign exchange rates. Time series data and technical indicators such as moving average, are fed to neural nets to capture the underlying "rules" of the movement in currency exchange rates. The trained recurrent neural networks forecast the exchange rates between American Dollar and four other major currencies, Japanese Yen, Swiss Frank, British Pound and EURO. Various statistical estimates of forecast quality have been carried out. Obtained results show, that neural ne…
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high frequency exchange rates of eight major world currencies over 2010-2018 period are used to study cross-correlations. The study is motivated by fundamental questions in complex systems' response to significant environmental changes and by potential applications in investment strategies, including detecting triangular arbitrage opportunities. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluc…
On Jan. 1, 1999 the European Union introduced a common currency Euro ($EUR$), to become the legal currency in all eleven countries which form the $EUR$. In order to test the $EUR$ behavior and understand various features, the $EUR$ exchange rate is artificially extrapolated back to 1993 by a linear superposition of the exchange rates of the 11 currencies composing $EUR$ with respect to several currencies not belonging to the $EUR$, i.e. Swiss Franc ($CHF$), Danish Kroner ($DKK$), British Pound ($GBP$), Japanese Yen ($JPY$) and U.S. Dollar ($USD$) of interest for reasons given in the text. The …
