Time series data often is observed with measurement error. One type of measurement error almost always present is rounding error. A procedure is proposed for estimating parameters of a finite moving average time series which is observed only after rounding. Method of moments estimators are proposed for estimation of parameters of time series observed with general measurement error, including error, ε_n, which is correlated with the series X_t being measured. This procedure requires knowledge of the autocovariance function (ACF) of ε_t, and the cross covariances between X_t and ε_r. For rounding error, the rounding error series is shown to approach uniform white noise as the rounding interval width, R, approaches zero, and the cross correlations between X_t, and rounding error ε_t, are shown to approach zero as R -> 0. For both small R and large R, the ACF of ε_t, and the cross covariances between X_t and ε_t, are approximated. These values are then used to estimate the parameters of the moving average model for X_t when X_t is observed after rounding. / Ph. D.