I found Everette Gardner's review of exponential smoothing to be very interesting. It is successful in presenting a broad view of the current state of exponential smoothing. The paper is noncontroversial in that its aim is to summarize previous research on exponential smoothing rather than to come to any definitive conclusions about the 'best' variant of exponential smoothing or the 'best' forecasting method. I would like to thank Gardner for doing an excellent job of organizing a vast amount of material in a readable manner. My discussion of the paper is concerned with a number of observations about exponential smoothing based upon the paper.
One thing that struck me is that there are many different forecasting methods which fall in the general category of exponential smoothing. For example, Exhibit 1 suggests that there are as many as 17 different versions. Why are there so many variations? One explanation is that there are many different types of time series behaviour occurring in the real world and each different method was designed to best forecast each different time series structure. Another explanation is that some of the variations are proposed solutions to time series behaviour which is perceived to exist by researchers who rarely or never deal with real data but in reality there are few time series for which these variations are relevant. Some of the variations may be able to be dismissed for this reason; however, based upon the popularity of exponential smoothing as a forecasting technique it is clear that many of the versions have some merit. Thus, an important question for the practitioner in need of a forecast method for a particular time series is: 'which of the variants of exponential smoothing is best for my particular data set? In a sense much of Gardner's paper is attempting to provide advice about this question.
My interpretation of the advice is that to pick the correct method, it takes experience, skill and some knowledge of the characteristics of the data you desire to forecast. A hypothetical practitioner may have to answer questions such as the following. Is your data seasonal? Is the seasonality additive or multiplicative? Does the data fluctuate locally around a constant level, or a linear trend, or a non-linear trend? How stable are the parameter estimates? Once these kinds of questions are answered a decision can be made about the particular variant of exponential smoothing that is appropriate. Then there are other more technical questions to answer. What values should be chosen for the smoothing parameters? What are the starting values? The review by Gardner suggests that there are a variety of opinions about these technical issues. Furthermore, the complexity of the issues seems to increase the more removed the methods get from the basic exponential smoothing models. My point is that unless a practitioner is willing to limit the possibilities to only the basic forms of exponential smoothing, the process which leads to getting the forecasts can apparently get very complicated. I suspect that experts in exponential smoothing have had a great deal of experience with real data and would admit that there is a great deal of skill involved in choosing the right alternative. If my suspicions are correct, I would argue that one of the virtues frequently claimed for exponential smoothing, its simplicity, may be illusory.
Suppose a practitioner is faced with the problem of choosing which approach within the realm of exponential smoothing methods will provide the best forecasts. One way to approach this problem is to arbitrarily select a simple form of exponential smoothing such as a non-seasonal constant level method or a non-seasonal linear trend method. Suppose this method is going to be applied to a number of time series. If some of the series' behaviour is inconsistent with what is implicitly