Microcomputers in Civil Engineering 12 (1997) 353–368 Determining Inputs for Neural Network Models of Multivariate Time Series H. R. Maier Senior Civil Engineer, Western Samoa Water Authority, P.O. Box 245, Apia, Western Samoa & G. C. Dandy * Department of Civil and Environmental Engineering, University of Adelaide, Adelaide 5005, Australia Abstract: In recent years, artificial neural networks have been used successfully to model multivariate water resources time series. By using analytical approaches to determine ap- propriate model inputs, network size and training time can be reduced. In this paper , it is proposed that the method of Haugh and Box and a new neural network–based approach can be used to identify the inputs for multivariate artificial neural network models. Both methods were used to obtain the inputs for a multivariate artificial neural network model used for forecasting salinity in the River Murray at Murray Bridge, South Australia. The methods were compared with a third method that uses knowledge of travel times in the river to identify a reasonable set of inputs. The results obtained in- dicate that all three methods are suitable for determining the inputs for multivariate time series models. However , the neu- ral network–based method is preferable because it is quicker and simpler to use. Any prior knowledge of the underlying processes should be used in conjunction with the neural net- work method. 1 INTRODUCTION Time series analysis methods have been used extensively to model hydrologic time series, water-quality time series, and water demand, water pricing, and meteorologic time series * To whom correspondence should be addressed. and are a vital tool in water resources planning and man- agement. 23 Traditionally, the ARMA (autoregressive moving average) class of models 5 has been used for modeling water resources time series because such models are “... accepted, standard representations of stochastic time series” 46 and are among those forecasting models applied most successfully in practice. 41 For example, this class of models has been used successfully to model river flows, 3,9,17,39,42,44 water levels, 26 and water-quality parameters. 9 In many instances, multivariate models are required to model the complex relationship between the input and out- put time series, since the output time series may depend not only on its own previous values but also on past val- ues of other variables. For example, water consumption de- pends on factors such as monthly rainfall, the number of rain days per month, monthly evaporation, and monthly av- erage temperature, 13 and river salinity at a particular location depends on upstream salinities, river levels, and flows. 34 An excellent review of the use of ARMA type models for model- ing multivariate water resources time series is given by Salas et al. 39 In recent years, artificial neural network (ANN) meth- ods have been applied successfully to a number of multi- variate forecasting problems in the field of water resources engineering. 13-15,30,31,34,47,48 ANNs are a form of computing inspired by the functioning of the brain and nervous system and are discussed in detail by a number of authors. 1,21,24,29,34 ANN models have a number of advantages over ARMA type © 1997 Microcomputers in Civil Engineering. Published by Blackwell Publishers, 350 Main Street, Malden, MA 02148, USA, and 108 Cowley Road, Oxford OX4 1JF, UK.