Exponential Smoothing

EXPONENTIAL SMOOTHING

Exponential smoothing was proposed in the late 1950s (Brown 1959, Holt 1957 and Winters 1960 are key pioneering works) and has motivated some of the most successful forecasting methods. Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation the higher the associated weight. This framework generates reliable forecasts quickly and for a wide spectrum of time series which is a great advantage and of major importance to applications in industry.

All leading methods of exponential smoothing involve the same essential process of data averaging. The data series to be forecast is assumed to be modeled by one, two, or three essential components. Key components represent:

* Level

* Trend

* Seasonality of data being forecast.

The level of the time series to be forecast is the average about which it fluctuates. This level may be constant or slowly changing.

Trend is any systematic change in the level of the time series of data. If a given forecast model includes a trend, then that trend is either projected as a straight line into the future or as a gradually diminishing amount that eventually dies out.

The seasonality of a time series is a pattern of change tied to weather, custom, or tradition. Retail sales typically exhibit a strong seasonal trend over the course of the year. Seasonal components can be additive, meaning that seasonal patterns remain constant over time, or multiplicative, meaning that seasonal patterns grow with the average level of the series.

A. One Parameter (Simple) Exponential Smoothing

In simple exponential smoothing, the sole regular component is the lvel of the forecast data series. It is implicitly assumed that the data consist of irregular fluctuations around a constant or very slowly changing level. Simple exponential...