Using wavelets for time series forecasting: Does it pay off?

By means of wavelet transform a time series can be decomposed into a time dependent sum of frequency components. As a result we are able to capture seasonalities with time-varying period and intensity, which nourishes the belief that incorporating the wavelet transform in existing forecasting methods can improve their quality. The article aims to verify this by comparing the power of classical and wavelet based techniques on the basis of four time series, each of them having individual characteristics. We find that wavelets do improve the forecasting quality. Depending on the data's characteristics and on the forecasting horizon we either favour a denoising step plus an ARIMA forecast or an multiscale wavelet decomposition plus an ARIMA forecast for each of the frequency components.