A wavelet-based method for time series forecasting

Usually time series are controlled by two or more data generative processes which display changes over time. Each one of these processes may be described by different models. In practice, the observed data is an aggregated view of the processes, fact which limits the effectivity of any model selection procedure. In many occasions, the data generative processes may be separated by using spectral analysis methods, reconstructing a specific part of the data by filtering bands. Then, a filtered version of the series may be forecasted, by using proper model selection procedures. In this article we explore the use of forecasting methods in the wavelet space. To do this, we decompose the time series into a number of scale time sequences by applying a discrete wavelet transform. By fitting proper ARIMA models at each resolution level, a forecasting step is conducted. Then, by applying the inverse wavelet transform, we reconstruct forecasted time series. Experimental results show the feasibility of the proposed approach.