Exponential smoothing with a damped multiplicative trend

Abstract

Multiplicative trend exponential smoothing has received very little attention in the literature.It involves modelling the local slope by smoothing successive ratios of the local level, and this leads to a forecast function that is the product of level and growth rate. By contrast, the popular Holt method uses an additive trend formulation. It has been argued that more real series have multiplicative trends than additive. However, even if this is true, it seems likely that the more conservative forecast function of the Holt method will be more robust when applied in an automated way to a large batch of series with different types of trend. In view of the improvements in accuracy seen in dampening the Holt method, in this paper, we investigate a new damped multiplicative trend approach. An empirical study, using the monthly time series from the M3-Competition, gave encouraging results for the new approach at a range of forecast horizons, when compared to the established exponential smoothing methods.

25 years of time series forecasting

“…McKenzie, 1984). The damped multiplicative methods of Taylor (2003) provide the only genuinely new exponential smoothing methods over this period. There have, of course, been numerous studies applying exponential smoothing methods in various contexts including computer components (Gardner, 1993), air passengers (Grubb & Masa, 2001) and production planning (Miller & Liberatore, 1993).…”

“…There have, of course, been numerous studies applying exponential smoothing methods in various contexts including computer components (Gardner, 1993), air passengers (Grubb & Masa, 2001) and production planning (Miller & Liberatore, 1993). Hyndman et al's (2002) taxonomy (extended by Taylor, 2003) provides a helpful categorization in describing the various methods. Each method consists of one of five types of trend (none, additive, damped additive, multiplicative and damped multiplicative) and one of three types of seasonality (none, additive and multiplicative).…”

“…Ord et al (1997) built on the work of Snyder (1985) by proposing a class of innovation state space models which can be considered as underlying some of the exponential smoothing methods. Hyndman et al (2002) and Taylor (2003) extended this to include all of the 15 exponential smoothing methods. In fact, Hyndman et al (2002) proposed two state space models for each method, corresponding to the additive error and the multiplicative error cases.…”

Forecasting and operational research: a review

“…Unfortunately, few commercial software packages yet include it. Smoothing methods have seen further innovations, including Taylor's (2003) multiplicative damped model leading to 15 variants of exponential smoothing. All the issues surrounding exponential smoothing are ably reviewed in Gardner (2006 This is equivalent to simple exponential smoothing (with trend = 0) and was developed by Harrison and Stevens (1971) into multi-state Bayesian Forecasting.…”

New approach to Forecasting Agro-based statistical models

“…For example, the major finding of [16], and [14], who used thousands of time series, was that simple methods, such as simple exponential smoothing and damped trend methods perform as well or in many cases better than those that are more statistically sophisticated ones like ARIMA models. The flexibility of exponential smoothing is demonstrated by its ability to provide forecasts for the complete taxonomy of [19], as extended by [11] and [22].…”