Some misconceptions about the behavior of weights in exponential smoothing

Exponential smoothing methods are presumed to generate exponentially decreasing weights to observations as they get older. However, this is true for only simple exponential smoothing models and not always true in general. This paper identifies and characterizes the situations where exponential smoothing methods give lesser weights to the more recent observations. The paper provides a mathematical proof that weights in exponential smoothing do not necessarily decrease exponentially for the double exponential smoothing case. The conditions under which weights decrease exponentially are identified, and necessary and sufficient conditions are spelt out. Example data from the literature are used to validate the present arguments. Also, a simple spreadsheet based analysis is discussed for generating the weights for double exponential smoothing.