A Dynamical System Applied to Foreign Currency Exchange Determination

Masaaki Yoshimori¹*, Hiroki Takada² and Takashi Matsugi³

¹Information Technology Center, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
²Graduate School of Science, Division of Material Science, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
³Department of Information and Policy Studies, Aichi-Gakuin University, Iwasaki-cho, Nisshin, Aichi 470-0131, Japan
*E-mail address: yoshimori2003@yahoo.com

(Received March 7, 2002; Accepted October 31, 2003)

Keywords: Exchange Rate, Correlation Dimension, Multiple Regression, Principal Component Analysis

Abstract. A problem of finding the number of variables describing monthly JP/US$ exchange rate is treated on the basis of fractal theory and principal component analysis. First, we calculated the correlation dimension of the exchange rate according to the idea that the time series of the exchange rate is composed of chaos. The correlation dimension proved to be a value of around 1.4, hence two variables are at most required. Secondly, two principal components were extracted by the multiple regression out of six economic variables. Lastly, we drew comparison the combination method based on the fractal theory and the principal component analysis.