In repeated surveys, the usual survey estimator of a characteristic can be represented as the sum of the true value and a measurement error, where the measurement error is due to sampling. If the sampling units stay in the survey for a fixed finite number of periods, then the sequence of sampling errors, \u[subscript]t, is a moving average. Assuming that the sequence of true values, \x[subscript]t is a realization of a time series, the objective of estimating the covariance structure of the series \x[subscript]t is considered;For the Current Population Survey, a components-of-variance model for the sampling error is estimated. Three components of variance are identified. These are a replicate component that is due to variation between primary sampling units, a permanent component associated with rotation groups within primary sampling units, and a transient component associated with rotation groups within primary sampling units. The replicate component and the permanent rotation group effects are assumed to be constant over time. The transient rotation group effect is assumed to be a third order autoregressive process. Under the 4-8-4 rotation scheme of the Current Population Survey, u[subscript] t is a fifteenth order moving average. Given the covariance function of \u[subscript]t, two estimation procedures of the structure of \x[subscript]t are proposed and applied to data from the Current Population Survey. The first procedure is a frequency domain estimation procedure and the second procedure uses autocovariances;The limiting distribution of the frequency domain estimator is derived. A Monte Carlo study of the estimator for the first order moving average is conducted. The distributional properties of the estimator and the asymptotic results are in reasonable agreement for samples on the order of 100 observations when the parameter is not close to the boundary.