Analysis of Non-Stationary Time Series using Wavelet Decomposition

Abstract: The increased computational speed and developments in the area of algorithms have created the possibility for efficiently identifying a well-fitting time series model for the given nonstationary-nonlinear time series and use it for prediction. In this paper a new method is used for analyzing a given nonstationary-nonlinear time series. Based on the Multiresolution Analysis (MRA) and nonlinear characteristics of the given time series a method for analyzing the given time series using wavelet decomposition is discussed in this paper. After decomposing a given nonstationary-nonlinear time series Zt in to a trend series Xt and a detail series Yt the trend series and the detail series are separately modeled. Model T(t) representing the trend series Xt and the Threshold Autoregressive Model of order k (TAR(k)) representing detail series Yt are combined to obtain the Trend and Threshold Autoregressive(T-TAR) model representing the given nonstationary-nonlinear time series. The scale dependent thresholds for the TTAR model are obtained using the detail series and using the trend series. Also simulation studies are done and the results revealed that the developed method could increase the forecasting accuracy. [Nature and Science 2010;8(1):53-59] ( ISSN: 1545-0740).