Noise reduction and prediction of hydrometeorological time series: dynamical systems approach vs. stochastic approach

Non-linear dynamical systems and linear stochastic approaches have been used to analyse synthetic and hydrometeorological time series. The analysis by dynamical systems approach include computation of the correlation dimension, noise reduction and non-linear prediction, while analysis by the linear stochastic approach include model identification, formulation, diagnostic tests and prediction. Computation of the correlation dimension of synthetic clean series have been done by Grassberger and Procaccia algorithm and other methods. An efficient method of neighbour search, which can be incorporated with Grassberger and Procaccia algorithm has been proposed. A set of artificially contaminated data sets with different levels of noise were created and different non-linear noise reduction techniques have been employed in these and the hydrometeorological time series. The correlation dimensions of cleaned series have been computed by efficient algorithms. Prediction of different time series was made by both approaches. Prediction accuracies, as well as the results of a test for the existence of determinism point to the conclusion that many of the seemingly stochastic series considered were deterministic.