Fractal dimensions and the Lyapunov exponents in the Philippine foreign exchange market

• Main Author: Khanser, Marites Ariola
• Format: text
• Language: English
• Published: Animo Repository 1998
• Subjects: Lyapunov exponents; Differential equations; Fractals; Dimension theory (Topology); Foreign exchange market > Philippines; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_doctoral/787
• Institution: De La Salle University

This dissertation is an empirical investigation of the P:US foreign exchange rate and volume trading behavior through the application of Chaos Theory. This nonlinear, financial analytical technique calls for the calculation of the correlation dimension as an estimate of the fractal dimension and the calculation of the correlation dimension as an estimate of the fractal dimension and the calculation of the largest positive Lyapunov exponent as an evidence that the time series is sensitive to initial conditions. A fractal structure and sensitivity to initial conditions are the basic characteristics of deterministic chaos.This study investigated the raw data from the Philippine currency market, consisting of the 1946-1997 (52-year period) daily P:US foreign exchange time series and daily volume trading data from 1988-1997. The daily time series and the volume trading data were detrended (or filtered) using the logarithmic transformation, specifically, the first differencing to prepare the data for chaos analysis. Then the detrended data were then subjected to chaos tests: the test for the fractal dimension using the correlation dimension and the test for chaotic behavior using the Lyapunov exponent estimation. The calculation of the correlation dimension made use of the concept of embedding dimensions or the Grassberger-Procaccia's algorithms while the calculation of the largest positive Lyapunov exponent made use of the Wolf algorithm. In addition to the major chaos tests, the data was also subjected to other chaos-related tests, namely: data manipulation, graph of data, probability distribution, polynomial fit, power spectrum, dominant frequencies, capacity dimension, correlation function, correlation matrix, phase-space plots, return maps, and Poincare movies. Results for the volume trading data show a correlation dimension between the 2 and 3, hence, a fractal dimension approximately between 2.941 and 3.840. This means that the volume trading time series has a fractal structure, revealed by a strange attractor found in the phase-space plots. A positive Lyapunov exponent was likewise found which is 0.114 of which its inverse provides the forecasting horizon for the prediction model. The same findings were likewise found in the 1946-1997 Peso-US dollar foreign exchange rate series, with positive Lyapunov exponent of 0.020 indicating the presence of deterministic chaos in the Philippine foreign exchange market.This research likewise developed a nonlinear, deterministic, chaos-based forecasting model using the singular value decomposition technique to predict future Peso-dollar foreign exchange rates movements and volume of trading on a daily basis.The study rejected the random walk model under the efficient market hypothesis, and validated the hypothesis that the Philippine foreign exchange market has a fractal structure that it exhibits sensitivity to initial conditions that the system is deterministic chaos, and therefore, the local market is a nonlinear dynamical system.