We develop a z-transform transfer function model of the Damped Trend forecasting mechanism from which we determine its stability boundary. We show that the Damped Trend forecasting mechanism is stable for a much larger proportion of the parametrical space than is currently acknowledged in the literature. We incorporate the Damped Trend forecasting mechanism into an Order-Up-To (OUT) replenishment policy and investigate the frequency response of this system. We prove that Naïve, Exponential Smoothing, and Holts forecasts, when used within the OUT policy, will always generate bullwhip, for every possible demand process, for any lead-time. However, the Damped Trend forecasting mechanism, when used within the OUT policy, behaves differently. Sometimes it will generate bullwhip and sometimes it will not. Bullwhip avoidance occurs when demand is dominated by low frequencies in some instances. In other instances, bullwhip avoidance happens at high frequencies. We are also able to demonstrate a complex odd-even lead-time effect exists. Bullwhip may be avoided when the lead-time is odd for a particular demand pattern but reappears when the lead-time changes to an even number. cases we obtain insights into the convexity and limit behaviour of the cost function. This allows us to gain knowledge of the number of minimums and, in some cases, upper and lower bounds on optimal parameter setting and costs incurred.