An autocorrelation function method for estimation of parameters of autoregressive models

Abstract

An autocorrelation function method was developed for estimating the parameters of autoregressive models. For monthly streamflow series, an ordinary least-squares method was used to optimally determine the parameters by minimizing the sum of the squares of differences between the autocorrelations calculated directly from the observed time series and those from the model-generated streamflow. The approach was tested using numerical simulation and historical data. Numerical results showed that for some generated data series the parameters estimated by the new method were closer to their true values than those obtained from the Yule-Walker equations. For monthly streamflow time series of three stations of Yellow River in China, the historical correlation functions were compared with those from data series generated with the AR(2) model. The autocorrelation function estimated from the generated data series was closer to the observed autocorrelation than that obtained from the Yule-Walker equations. This is even more true for the multivariate autoregressive model.