The comprehensive survey of the state of the art in exponential smoothing by Gardner was impressive on my first reading. When asked by the editors to organize commentaries on the paper, I was happy to take on this task, given my perception of its importance.
Although much of the paper is not controversial, it was nevertheless desired that the widest range of people be contacted and asked to comment. Nine experts in the topic area with a variety of perspectives were invited to formally comment on the paper. Practitioners as well as academics were represented. Some were closely identified with early developments in the area of exponential smoothing, and others were associated with continuing developments in the ARI MA modeling area. Several of those invited to comment did not submit formal commentaries but did review the work very favourably and provided reactions directly to Gardner. In some cases, these comments were incorporated in the manuscript.
The commentaries which follow present Gardner's paper, I believe, in the proper perspective. As McKenzie states, the paper contributes greatly to our understanding of the development of smoothing procedures as well as our understanding of their properties. Knowledge of these properties can, as Chatfield points out, help practitioners sort out which procedures might be applied in a given situation. This selection problem is sometimes difficult and Hillmer's agreement with Gardner on the need for an organized approach to the selection of a smoothing variant seems reasonable and suggests potential future research avenues.
I would like to add an additional comment. Early work, including some by myself, into the identification of ARIMA equivalents to exponential smoothing has sometimes been incorrectly characterized as revealing the 'inferiority' of smoothing procedures, since in many cases an exponential smoothing model is demonstrably a special case of a broad class of ARIMA models. This characterization is not shared by me. Analytically, it was shown in an early paper that smoothing procedures are rather robust. Thus, their 'inferiority' in a practical sense has not been supported. The importance of knowing what these ARIMA equivalences are, however, cannot be overemphasized. Any progress in developing objective selection procedures for exponential smoothing will probably benefit from this work, which is fully described in Gardner's paper. A further important point on model equivalencies is that I have come to the point of view, since the development of damped trend smoothing, and other variants, that every ARIMA model can probably be described in exponential smoothing terminology. There are exponential smoothing models which have no ARIMA equivalent (e.g. Winters multiplicative seasonal smoothing) as well as models which have very non-parsimonious ARIMA equivalents (e.g. Winters additive seasonal approach). Thus, the debate is not over between provincial advocates of