An informational approach to model time series of environmental data through negentropy estimation

A methodology based on the minimum negentropy criterion (minimum cross-entropy) is proposed, which enables one to determine the optimal order of a model candidate to reproduce the behaviour of time series of environmental data. The procedure, which involves the computation of the prediction error, represents a unifying approach of conventional and inferential statistics and permits at the same time to account for all informational content embodied in the data and it avoids both underfitting and overfitting of experimental observations, thus guaranteeing the principle of model's parameter parsimony and balanced accuracy. Following the theoretical derivation of the approach, the method is verified through harmonic analysis of data sets collected in the lagoon of Venice and exhibiting high variability: surface data temperature, exceptional tidal observations, chlorophyll a and ammonia concentrations. Extensions of the procedure to other type of data and of class of model, are also prospected.