Autoregressive Empirical Modelling of Multiple Precipitation Time Series

Abstract

Autoregressive (AR) data models are implied in many analytical procedures used in the description and interpretation of hydrologic data sets. The maximum entropy method (MEM) of spectral estimation is equivalent to the AR representation of the data. The paper presents a new algorithm for spectral estimation based upon the MEM approach and is applied to multiple precipitation time series. The algorithm is similar to generalizations of the Burg method for multichannel data. The new approach independently estimates the forward and backward prediction error powers in terms of the current but yet undetermined forward and backward prediction error filters (PEF). The new approach accomplishes then an averaging of the two available autocorrelations coefficients estimates, which minimize the forward and backward prediction error powers. The methodology is applied to the Grand River Basin in southern Ontario, Canada. In particular, six precipitation stations sampled at 15-day intervals are used for numerical analysis. The length of the PEF was 10 points.