Time Series Analysis with Wavelet Coefficients

Time series are conventionally analyzed only in the time domain or only in the frequency domain, and few analyses make use of information in both domains simultaneously. On the other hand, time series analysis based on the wavelet transform has been concentrated on the irregularity detection or the analysis of stochastic processes constructed by the wavelet transform. The wavelet transform is applied to stationarity analysis and predictions in the present paper. Using the wavelet transform, we can decompose time series into frequency components. Consequently, we can extract local information with respect to frequency. We observe the time series in both the time domain and the frequency domain simultaneously. And we connect weak stationarity and prediction methods of original time series to those of each frequency component, accompanied with numeric results.