The importance of adaptive and exponentially smoothed forecasting has led to the development of several schemes using the tracking signal or the smoothed autocorrelation function for changing the value of the smoothing coefficient. An alternative scheme, using evolutionary spectra is proposed. The smoothing constant is determined as a function of the maximum change in the various frequency components of successive spectra. The location and magnitude of this maximum change also indicates the type of disturbance in the underlying stochastic process generating the series. Simulation experiments indicate that the use of spectra in this evolutionary fashion produces forecasts that are generally more stable as well as more sensitive to genuine changes than schemes based on the tracking signal.