We investigate some statistical properties of ac voltages from a white noise source measured with a digital lock-in amplifier equipped with finite impulse response output filters which introduce correlations between successive voltage values. The main goal of this work is to propose simple solutions to account for correlations when calculating the standard deviation of the mean (SDM) for a sequence of measurement data acquired using such an instrument. The problem is treated by time series analysis based on a moving average model of the filtering process. Theoretical expressions are derived for the power spectral density (PSD), the autocorrelation function, the equivalent noise bandwidth and the Allan variance; all are related to the SDM. At most three parameters suffice to specify any of the above quantities: the filter time constant, the time between successive measurements (both set by the lock-in operator) and the PSD of the white noise input, h₀. Our white noise source is a resistor so that the PSD is easily calculated; there are no free parameters. Theoretical expressions are checked against their respective sample estimates and, with the exception of two of the bandwidth estimates, agreement to within 11% or better is found.