Cascade Model of Monthly Municipal Water Use

A time series model of monthly municipal water use is formulated as a set of equations representing the effects of four factors on water use: trend, seasonality, autocorrelation, and climatic correlation. The parameters of these equations are found by passing the water use time series through a cascade of four transformations; in each transformation the parameters of an equation associated with one factor are statistically determined and the series transformed to remove the effects of this factor. After the last transformation, only a random error series remains. Monthly municipal water use at Canyon, Texas, from 1961–1978 is modeled as an example. The model explains 86% of the variance of this series, divided among the four factors as trend (29%), seasonality (44%), autocorrelation (2%), and climatic correlation (11%). The random error is shown to be normally distributed by a nonparametric procedure characterizing probability families by their density quantile functions.