The Wiener-Kolmogorov (WK) signal extraction filter, extended to handle nonstationary signal and noise, has minimum Mean Squared Error (MSE) for Gaussian processes. However, the stochastic dynamics of the signal estimate typically differ from that of the target. The use of such filters, although widespread, has been observed to produce dips in the spectrum of the seasonal adjustments of seasonal time series. These spectral troughs correspond in practice to negative autocorrelations at lag 12 (or negative seasonal autocorrelation), a phenomenon corresponding to an annual stochastic cycle. So-called "square root" WK filters were introduced by Wecker (1979) in the case of stationary signal and noise, to ensure that the signal estimate shared the same stochastic dynamics as the original signal, and thereby remove spectral dips. This represents a different statistical philosophy: not only do we want to closely estimate a target quantity, but we desire that the dynamics of our estimate closely resemble those of the target. The MSE criterion ignores this aspect of the signal extraction problem, whereas the "dynamic matching" filters account for this issue at the cost of accruing additional MSE. This paper provides empirical documentation of the occurrence of negative seasonal autocorrelation in seasonally adjusted data, and provides matrix formulas for filters that match the dynamics of the desired signal, and are appropriate for finite samples of nonstationary time series. We apply these filters to 88 time series to produce seasonal adjustments that have greatly reduced incidents of negative seasonal autocorrelation.