Pritha Das

Chaotic analysis of the foreign exchange rates

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.

Chaos in a three dimensional neural network

Abstract An artificial neural network (ANN) consisting of three neurons has been considered. The equations of control are given by three differential equations (DE) with nonlinear, positive and bounded response functions of the neurons. Bifurcation diagram and three dimensional (3-D) phase portraits of the model show rich dynamics. With the change in synaptic weight and decay rate, the system passes from stable to periodic and then chaotic regimes. Interestingly, the system returns to periodic regime by further changing the synaptic weight. Computer code to calculate the Lyapunov exponent (LE) has been written to confirm chaos.

Stability and oscillations of a negative feedback delay model for the control of testosterone secretion

A modified time-lag model for the control of the secretion of the hormone testosterone is proposed. Conditions for switching of the steady state from stable to unstable are derived. Questions concerning small amplitude oscillations of solutions are addressed analytically and numerically.

Does composite index of NYSE represents chaos in the long time scale

Abstract Here we analyze the Composite Index (CI) for 32 years, from 1966 to 1997 of the New York Stock Exchange (NYSE). Individual share prices may be unpredictable—is it true for CI also—particularly in the time scale of 32 years? In the first half (consisting first 16 years) CI is confined to values in the range of 36–75 and in the second half, it rises to 600 point mark. Non-linear analysis of data confirms that CI is not unpredictable in longer time scales. Moreover, the second half of the data fits well with some growing function of time.

FRACTAL ANALYSIS OF DIFFERENT EASTERN AND WESTERN MUSICAL INSTRUMENTS

In this paper, we attempt musical analysis by measuring fractal dimension (D) of musical pieces played by several musical instruments. We collected solo performances of popular instruments of Western and Eastern origin as samples. We attempted usual spectral analysis of the selected clips to observe peaks of fundamental and harmonics in frequency regime. After appropriate processing, we converted them into time series data sets and computed their fractal dimension. Based on our results, we conclude that instrumental musical sounds may have higher Ds than those computed from vocal performances of different types of Indian songs.

Nonlinear data analysis of experimental (EEG) data and comparison with theoretical (ANN) data

In this article, nonlinear dynamical tools such as largest Lyapunov exponents (LE), fractal dimension, correlation dimension, pointwise correlation dimension will be used to analyze electroencephalogram (EEG) data obtained from healthy young subjects with eyes open and eyes closed condition with the view to compare brain complexity under this two condition. Results of similar calculations from some earlier works will be produced for comparison with present results. Also, a brief report on difference of opinion among coworkers regarding such tools will be reported; particularly applicability of LE will be reviewed. The issue of nonlinearity will be addressed by using surrogate data technique. We have extracted another data set that represented chaotic state of the system considered in our earlier work of mathematical modeling of artificial neural network. We further attempt to compare results to find nature of chaos arising from such theoretical models.

Investigating the Existence of Chaos in Inflation Data in relation to Chaotic Foreign Exchange Rate

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, and so forth. In a series of works, 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 would like to address the specific question, Is inflation data 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.

Comparison of the Nature of Chaos in Experimental [EEG] Data and Theoretical [ANN] Data

In this paper, nonlinear dynamical tools like largest Lyapunov exponents (LE), fractal dimension, correlation dimension, pointwise correlation dimension will be employed to analyze electroencephalogram [EEG] data and determine the nature of chaos. Results of similar calculations from some earlier works will be produced for comparison with present results. Also, a brief report on difference of opinion among coworkers regarding tools to characterize chaos will be reported; particularly applicability of LE will be reviewed. The issue of nonlinearity present in experimental time series will be addressed by using surrogate data technique. We have extracted another data set which represented chaotic state of the system considered in our earlier work of mathematical modeling of artificial neural network. By comparing the values of measures employed to the two datasets, it can be concluded that EEG represents high dimensional chaos, whereas the experimental data due to its deterministic nature, is of low dimension. Also results give the evidence that LE exponent is applicable for low dimensional chaotic system while for experimental data, due to their stochasticity and presence of noise‐ LE is not a reliable tool to characterize chaos.