EXPLORATORY SPECTRAL-ANALYSIS OF HYDROLOGICAL TIMES SERIES

Current methods of estimation of the univariate spectral density are r eviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data an alysis (EDA) tool which complements, rather than competes with, the po pular ARMA model building approach. A new diagnostic check for ARMA mo del adequacy based on the nonparametric spectral density is introduced . Additionally, two new algorithms for fast computation of the autoreg ressive spectral density function are presented. For improving interpr etation of results, a new style of plotting the spectral density funct ion is suggested. Exploratory spectral analyses of a number of hydrolo gical time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral anal ysis to determine the possible existence of long memory in natural tim e series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densit ies suggests the ARMA models fitted previously to these datasets adequ ately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.sta ts.uwo.ca.