A Wavelet Transform Approach to Chaotic Short-Term Forecasting

Abstract

Chaos theory is widely employed to forecast near-term future values of a time series using data that appear irregular. The chaotic short-term forecasting method is based on Takens’ embedding theorem, which enables us to reconstruct an attractor in a multi-dimensional space using data that appear random but rather are deterministic and geometric in nature. It is difficult to forecast future values of such data based on chaos theory if the information that the data provide cannot be reconstructed through wavelet transformation in a sufficiently low-dimensional space. This paper proposes a method to embed data in a small-dimensional space. This method enables us to abstract the chaotic portion from the focal data and increase forecasting precision.

Chaotic methods are employed to forecast near-term future values of uncertain phenomena. The method makes it possible to restructure an attractor of given timeseries data set in a multidimensional space using Takens’ embedding theory. However, many types of economic time-series data are not sufficiently chaotic. In other words, it is difficult to forecast the future trend of such economic data even based on chaos theory. In this paper, time-series data are divided into wave components using a wavelet transform. Some divided components of time-series data exhibit much more chaotic behavior in the sense of correlation dimension than the original time-series data. The highly chaotic nature of the divided components enables us to precisely forecast the value or the movement of the time-series data in the near future. The up-and-down movement of the TOPICS value is shown to be well predicted by this method, with 70% accuracy.