Application of a local linear autoregressive model to BOD time series

In this paper, we analyze the biochemical oxygen demand data collected over two years from McDowell Creek, Charlotte, North Carolina, U.S.A., by fitting an autoregressive model with time-dependent coefficients. The local linear smoothing technique is developed and implemented to estimate the coefficient functions of the autoregressive model. A nonparametric version of the Akaike information criterion is developed to determine the order of the model and to select the optimal bandwidth. We also propose a hypothesis testing technique, based on the residual sum of squares and F-test, to detect whether certain coefficients in the model are really varying or whether any variables are significant. The approximate null distributions of the test are provided. The proposed model has some advantages, such as it is determined completely by data, it is easily implemented and it provides a better prediction. Copyright (C) 2000 John Wiley & Sons, Ltd.