Description of periodic variation in parameters of hydrologic time series

The multivariate approach of marginal distributions and their sequential dependence models is often used for description of periodic-stochastic hydrologic time series. This is a nonfunctional (or nonparametric) method of description of periodic variation in basic parameters. Usually, it requires a large number of estimated parameters. This often represents a lack of respect for the sound statistical principle of parsimony in the total number of model parameters. Two distortions result from this approach when new samples are generated by these models. First, some estimates vary less in generated samples than they should. Second, a tendency exists to generate new extremes at the times of historic extremes, with some of them more pronounced than the historic extremes. The fitted Fourier functions with a limited number of significant harmonics to the periodic variation of basic parameters, as the functional (or parametric) description of periodicity in time series, require a much smaller total number of parameters. They either avoid or minimize the distortions in generated samples.