Exploratory spectral analysis of hydrological times series

Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.