HW-DDS: A Multiplicative Holt-Winters Method with a Damped Double-Smoothed Trend Estimator

The multiplicative Holt–Winters method estimates its trend by exponentially smoothing successive level differences, a single-pass recursion that inherits the noise contained in each level update. We propose HW-DDS, a variant in which the trend is instead obtained by applying Brown’s double smoothing to the level itself, together with a damping factor. Because the level carries the trend as a growing quantity, the lag between the single- and double-smoothed level recovers the slope directly, whereas the same construction applied to the level difference would collapse. Three properties are established: the trend estimator is asymptotically unbiased for the slope of a linear trend, so the undamped method yields unbiased forecasts; the recursion is asymptotically stable for every admissible parameter value; and under independent level noise the double-smoothed trend has strictly smaller variance than the Holt–Winters trend, by a factor given in closed form, between roughly 0.06 and 0.42 over the practical parameter range. Simulation confirms both asymptotic results to within numerical tolerance and delimits them under estimated seasonality, autocorrelated noise and structural breaks. On five real monthly series the method is broadly competitive with the Holt–Winters variants: across thirty rolling-origin comparisons no difference in predictive accuracy survives correction for multiple testing.