Bayesian-combined wavelet regressive modeling for hydrologic time series forecasting

Wavelet regression (WR) models are used commonly for hydrologic time series forecasting, but they could not consider uncertainty evaluation. In this paper the AM-MCMC (adaptive Metropolis-Markov chain Monte Carlo) algorithm was employed to wavelet regressive modeling processes, and a model called AM-MCMC-WR was proposed for hydrologic time series forecasting. The AM-MCMC algorithm is used to estimate parameters’ uncertainty in WR model, based on which probabilistic forecasting of hydrologic time series can be done. Results of two runoff data at the Huaihe River watershed indicate the identical performances of AM-MCMC-WR and WR models in gaining optimal forecasting result, but they perform better than linear regression models. Differing from the WR model, probabilistic forecasting results can be gained by the proposed model, and uncertainty can be described using proper credible interval. In summary, parameters in WR models generally follow normal probability distribution; series’ correlation characters determine the optimal parameters values, and further determine the uncertain degrees and sensitivities of parameters; more uncertain parameters would lead to more uncertain forecasting results and hard predictability of hydrologic time series.