Neighbourhood selection for local modelling and prediction of hydrological time series

The prediction of a time series using the dynamical systems approach requires the knowledge of three parameters; the time delay, the embedding dimension and the number of nearest neighbours. In this paper, a new criterion, based on the generalized degrees of freedom, for the selection of the number of nearest neighbours needed for a better local model for time series prediction is presented. The validity of the proposed method is examined using time series, which are known to be chaotic under certain initial conditions (Lorenz map, Henon map and Logistic map), and real hydro meteorological time series (discharge data from Chao Phraya river in Thailand, Mekong river in Thailand and Laos, and sea surface temperature anomaly data). The predicted results are compared with observations, and with similar predictions obtained by using arbitrarily fixed numbers of neighbours. The results indicate superior predictive capability as measured by the mean square errors and coefficients of variation by the proposed approach when compared with the traditional approach of using a fixed number of neighbours.