SPECTRAL ANALYSIS WITH REGULARLY MISSED OBSERVATIONS

0. Summary. Estimating the spectral density of a discrete stationary stochastic process is studied for the case when the observations consist of repeated groups of a equally spaced observations followed by 13 missed observations, (a > ,3). The asymptotic variance of the estimate is derived for normally distributed variables. It is found that this variance depends not only on the value of the spectral density being estimated, but also on the spectral density at the harmonic frequencies brought in by the periodic method of sampling. Curves are presented for ,B = 1 showing the increase in the standard deviation and effective decrease in sample size as a function of a. 1. Introduction. When observing a stationary stochastic process at equally spaced intervals of time, it is sometimes necessary to occasionally miss observations for calibration or other purposes. The difficulty of estimating the spectral density in this case is not greatly increased, but in order to determine what is lost by this method of sampling, it is necessary to determine the increase in variance. Given a sample of size N, X1, X2, ***, XN, from a real stationary stochastic process of mean zero and continuous spectral density, 00