Wavelet-Based Time Series Modeling For The Exchange Rates

Abstract

This paper proposes a new approach to analyze the exchange rates. Two kinds of methods, based on the wavelet theory, are applied to the time series and fitted using ARIMA modeling. First method is Wavelet Decomposition. The series are decomposed into wavelet coefficients by Multiresolution Analysis (MRA). One of significant wavelet coefficients is fitted by ARIMA model. Second method is EbayesThresh package. Series with removed noise through threshold are also fitted. To illustrate the usefulness of our methodology, we carry out an empirical application using the Korean exchange rates relatives to US dollar, Yen and Euro. By comparing models after two treatments with the model of raw data, this paper will find how effectively wavelet decomposition and EbayesThresh work to explain the data. Therefore, we conclude that MRA and EbayesThresh extract important information from the original data and help us to look into the data with a new angle.