Time Series Analysis of Grey Forecasting Based on Wavelet Transform and Its Prediction Applications

Grey forecasting based on GM (1,1) has become an important methodology in time series analysis. But due to the limitation of predicting non-stationary time series, an improved grey forecasting GM (1,1) model with wavelet transform was proposed. The time series data was first decomposed to different scales by wavelet transform with a trous algorithm previous of Mallat algorithm in the parallel movement of time series, and then the decomposed time series were forecasted by GM (1,1) model to obtain forecasting results of the original time series. Time series prediction capability of GM (1,1) combined with wavelet transform was compared with that of traditional GM (1,1) model and autoregressive integrated moving average (ARIMA) model to energy source consumption and production forecasting in China. To effectiveness of these methods, eighteen years of time series records (1985 to 2002) for energy source consumption and production were used. The forecasting result from GM (1,1) model with wavelet transform for the data from 2000 to 2002 presented highest precision of three models. It shows that the GM (1,1) model with wavelet transform is more accurate and performs better than traditional GM (1,1) and ARIMA model.