BOOTSTRAP PROCEDURES FOR TIME-SERIES ANALYSIS OF BOD DATA

Recently, Hannan studied the resolution of closely adjacent spectral lines. In the paper, he discusses the problem of determining the parameters of a trigonometric polynomial when it is observed with stationary noise. He also obtains the asymptotic properties of the estimates of these parameters. The purpose of this paper is to fit a trigonometric polynomial to a Biochemical Oxygen Demand (BOD) data set and to examine the sampling properties of the estimates of the parameters of the model by using the empirical bootstrap procedure. In particular, 95% bootstrap confidence intervals of the estimates are obtained. We also employ the Bayesian bootstrap technique to obtain the interval estimates of the parameters. The problem of prediction using the empirical and Bayesian bootstrap procedures is also studied. This model, when compared with time series models of the form ARIMA (p, d, q), gives better fit in terms of a lower mean squared error (MSE).