A spectral method for estimating parameters in rainfall models

Abstract

One of the most difficult problems in rainfall modelling is often the fitting of theoretical models to data. In this paper a spectral approach is proposed for fitting single-site models, by considering the approximate likelihood functions of collections of sample Fourier coefficients. An objective function is derived, which is the same as that used in Whittle's method for time series parameter estimation, and is shown to have an interpretation as a quasi-likelihood when the time series is non-Gaussian. The method requires knowledge of the theoretical spectral density of models to be fitted; the form of this spectral density is given for a wide class of point-process-based rainfall models. A variant of the method is also developed for when a number of independent replications of a rainfall process are available. Large-sample properties of the estimators are derived, and the method is illustrated with some data from the south-west of England.