A stepwise time series regression procedure for water demand model identification

摘要

Annual time series water demand has traditionally been studied through multiple linear regression analysis. Four associated model specification problems have long been recognized: (1) the length of the available time series data is relatively short, (2) a large set of candidate explanatory or “input” variables needs to be considered, (3) input variables can be highly correlated with each other (multicollinearity problem), and (4) model error series are often highly autocorrelated or even nonstationary. A step wise time series regression identification procedure is proposed to alleviate these problems. The proposed procedure adopts the sequential input variable selection concept of stepwise regression and the “three‐step” time series model building strategy of Box and Jenkins. Autocorrelated model error is assumed to follow an autoregressive integrated moving average (ARIMA) process. The stepwise selection procedure begins with a univariate time series demand model with no input variables. Subsequently, input variables are selected and inserted into the equation one at a time until the last entered variable is found to be statistically insignificant. The order of insertion is determined by a statistical measure called between‐variable partial correlation. This correlation measure is free from the contamination of serial autocorrelation. Three data sets from previous studies are employed to illustrate the proposed procedure. The results are then compared with those from their origi