Nonlinear Dependencies And Chaos In The Bilateral Exchange Rate Of The Dollar

Applied mathematics and computation, 2007

In this work, we investigate chaotic property of Foreign Exchange Rates of several countries. The foreign exchange market is a 24-h financial market. The trading in the foreign exchange markets generally involves the US dollar. Some of the related earlier works found evidence of chaotic structures in foreign exchange rates, some studies found little evidence of chaos, however, many of them showed evidence of nonlinear structure. This type of conflicting claims are common in nonlinear analyses of financial data, as shown in our earlier work (2006). For the present work, daily data were collected for twelve countries, mostly over the period January 1971 to December 2005. We have thus a time series of more than 8500 points for each country. Changes in the exchange rate are related to news in the fundamentals, but previous studies showed that the nature of the relation is nonlinear. We test the nonlinearity by the foreign exchange data by surrogate method and find different degree of nonlinearity for different countries. By measuring the largest Lyapunov exponent (LLE), we found indication of deterministic chaos in all exchange rate series. We attempted to find how foreign exchange relates to fundamental news like balance of payment to US dollar. Finally, we comment on limitation of LLE to report the dynamics of the time series.

Atin Das, Pritha Das and Gürsan Çoban AJBM Vol. 6(15), pp. 5226-5233, 18 April, 2012

We investigated chaotic property of foreign exchange rates (ForExRate) of several countries in which daily data where considered for twelve countries (Das and Das, 2007), mostly over the period January 1971 to December 2005. Everyone is aware of the acute recession into which the world economy entered since around July 2008. To investigate what effect this has on ForExRate of different countries, here we concentrated on data during the period of January 2008 to December 2009. Here we calculated the largest Lyapunov exponent (LLE) and compared the changes in its values before and during the recession period. We find that our earlier classification of countries based on LLEs holds true. Also we can conclude that the more nonlinear structure its foreign exchange rate shows the more its LLE changes. We also examined the relation of balance of trade (BoT) -being one of the fundamental news with financial market to ForExRate. For some countries, the ForExRate is falling sharply as BoT is increasing in the same period. The BOT curves for of all the countries considered here show that the US was facing less exports to other countries which may indicate the advent of a recession era.

J. Contemp. Manag., 2013

Chaotic processes are characterized by positive Lyapunov Exponent (LE)s as LE measures the rate at which information is lost from a system. We consider here the chaotic analysis of Foreign Exchange (ForEx) market data. Our previous works (2007, 2012) made nonlinear data analysis of the data during period before recession (up to 2005), and then investigated data from the same 12 countries for the periods of January 2008 to October 2009, to assess the effect of recession. In these works, we calculated the largest LE (LLE)s during recession and compared them with the LLE found before onset of recession. It was concluded that for a country, the more nonlinear structure its foreign exchange rate shows the higher LLE changes. Four years after the eruption of the global financial crisis, the world economy is still struggling to recover. During 2012, global economic growth has weakened further. In this context, this paper reinvestigates the daily ForEx market data again of the same twelve countries as well as European Union (EU) region for the period of Jan, 2009 to March, 2013. Here this paper finds that LLE values have increased over previous two years, implying that ForEx market may have become more chaotic. Also, LLE values are slowly approaching their pre-recession values which may be positive aspect for the ForEx market. Gross Domestic Product (GDP) growth rate of selected countries are also compared to address this finding. As before, the balance of trade (BoT) of these countries is investigated with the US.

Economics Research International, Volume 2014 (2014), Article ID 783505,, 2014

Foreign Exchange (ForEx) rates are amongst the most important economic indices in the international monetary markets. ForEx rate represents the value of one currency in another and it fluctuates over time. It is related to indicators like Inflation, Interest rate, Gross Domestic Product etc. In a series of work, we investigated and confirmed the chaotic property of ForEx rates by finding positive Largest Lyapunov Exponent (LLE). As Inflation influences ForEx, in this work we like to address the specific question: Is inflation data is also chaotic? We collected data for time period of 2000 to 2013 and tested for nonlinearity in data by surrogate method. Calculating LLE, we find existence of chaos in inflation data for some countries.

Physica A: Statistical Mechanics and its Applications, 2002

Journal of Macroeconomics, 2006

This short paper is a comment on "Univariate tests for nonlinear structure" by Catherine Kyrtsou and Apostolos Serletis. We summarize their main results and discuss some of their conclusions concerning the role of outliers and noisy chaos. In particular, we include some new simulations to investigate whether economic time series may be characterized by low-dimensional noisy chaos.

This study tests for the presence of nonlinear dependence and deterministic chaos in the rate of returns series for six Indian stock market indices. The overall result of our analysis suggests that the returns series do not follow a random walk process. Rather it appears that the daily increments in stock returns are serially correlated and the estimated Hurst exponents are indicative of marginal persistence in equity returns. Result from test of independence on filtered residuals suggests that the existence of nonlinear dependence, at least to some extent, can be attributed to the presence of conditional heteroskedasticity. It appears, therefore, that low order GARCH–type models can adequately explain some, but not all, of the observed nonlinear dependence in the data. The existing nonlinearity in the data appears to be multiplicative in nature. Further, we find very little evidence to support the proposition that returns are generated by a chaotic system. Only in two out of six ca...

Pritha Das, Atin Das, and Gursan Coban Chaotic Modeling and Simulation (CMSIM) 3: 509{517, 2012

In this work we evaluate the notable results of four interrelated successive works ([2{5]) dealing with the classification properties and temporal evolution of foreign exchange rates series (ForEX). The main idea in these works can be conceptualized through the behavior of the exponential divergence curves of financial time series that make a clear distinction for both spatial (between countries) and temporal (between different time segments of ForEX series) patterns. Despite being a well known concept, the use of exponential divergence curves for the classification of ForEX series is a relatively new concept. The classification procedure discussed here is based on the surrogate testing procedure where the statistics gathered from the original system is compared to the ones that are gathered from a completely randomized system. Our new researches on the data during the period of present economic recession (January 2008-October 2009) by calculating the largest Lyapunov exponent (LLE) has shown that the earlier classi cation of countries based on LLE's holds true. By a similar approach, we have investigated the temporal evolution of the exponential divergence distance metrics where we have developed a computationally consistent procedure to obtain the metrics for various ForEX series. Finally we obtained strong indicators for the distinction of the temporal evolution of ForEX series for developed and developing countries. We discuss possible reasons for the existing separation of temporal structures.

International Journal of Forecasting, 1996

This paper investigates the dynamic properties of high frequency foreign exchange rate returns. Using hourly data for four exchanges rates, the British Pound, the Deutschemark, the Japanese Yen and Swiss Franc, we attempt to differentiate between stochastic and deterministic behavior in hourly rates of returns. While the autocorrelation coefficients and the Brock-Dechert-Scheinkman test point to the presence of some non-linear dependence, correlation dimension estimates reveal little evidence in favor of low-dimensional chaos. The analysis appears to support the view that although it is not possible to exploit deterministic non-linear dependence in exchange rate time series in order to improve short-term forecasting, non-linear stochastic models can be used for conditional volatility forecasts.

Chaos Theory and Applications

A time series data contains a large amount of information in itself. Chaos data and volatility data which calculated by any time series are also derivative information included in the same time series. According to these assumptions, it is very important to question the ability of chaos and volatility information to affect each other, and which information affects and which information is affected. It is very important to determine the causes of volatility, which is an important result indicator for the finance literature, and especially with this study, it was tried to determine whether the chaos data is in a causal relationship with volatility. If some of the chaos data can be identified as the cause of volatility, the detected chaos data can be used in other research as a leading indicator of volatility. The data set used in the study is the daily euro/dollar exchange rate index between 01.01.2005 and 10.11.2022. In the study, time series of chaos data were created with Windowed ...