The exponential smoothing (ES) methodology chooses one from a small group of models which focus upon the trend and seasonal behavior of the data. Because those two aspects dominate the variance of the series, properly chosen ES models perform well relative to more complicated methods on a wide range of data series.

 

These techniques were designed for dealing with data where there is a smooth “signal” obscured by substantial measurement noise. While they can adequately capture many economic data series, they do it primarily by not smoothing at all. In fact, it isn’t uncommon for the a parameter, which governs the amount of smoothing, to have an optimal value bigger than 1 which means that past data are overweighted. This typically arises because the data have been time-averaged. If, for instance, a monthly series is constructed as an average of daily values, a sudden change late in the month won’t fully be reflected in the observed data until the next period.

 

Advantages

ES techniques are computationally simple, so you can quickly apply them to a large number of series. Plus, the small set of choices simplify the process of choosing the “best” ES model and make them ideal for very small data sets.

 

Disadvantages

The class of models is too narrow for some data series. For instance, a “no trend” model actually is a random walk model, so its forecasts remain at the final smoothed level. For series which return to a mean level, this behavior is very bad, especially at longer horizons. Also, when you have enough data to entertain a richer class of models, other methods are likely to do better.

 

Using the ESMOOTH Instruction

The ESMOOTH instruction implements exponential smoothing. You can type in the instruction directly, or you can use the Time Series>Exponential Smoothing Wizard to generate it.

 

You will need to choose both the trend model and the seasonal model, and decide between setting the smoothing parameters yourself or estimating them. You choose the models with the TREND and SEASONAL options on ESMOOTH. The choices available for these are:

 

trend=[none]/linear/exponential/select

seasonal=[none]/additive/multiplicative/select

 

If you choose SELECT, RATS will test all three choices for that option and select the best fitting model.

 

You can set the smoothing parameters with the ALPHA, GAMMA, and DELTA options (all default to 0.3), or you can use the ESTIMATE option to have RATS estimate the parameters. With ESTIMATE, RATS chooses the parameters by minimizing the in-sample squared one-step forecast errors. If you have a small amount of data (twenty or fewer data points), you should not try to estimate. Setting the parameters to reasonable values will usually be superior to relying upon imprecise estimates.

 

Examples

EXPSMOOTH1.RPF uses ESMOOTH to forecast a pair of U.S. interest rates.

 

EXPSMOOTH2.RPF uses it to “seasonally adjust” Canadian retail sales, letting ESMOOTH choose the form of both the trend and the seasonal.

 

Copyright © 2026 Thomas A. Doan