Exponential smoothing methods are suitable for non-stationary data (that is, data with a trend and/or seasonality) and work similarly to exponential moving averages. The forecasts are weighted averages of past observations. These models put more emphasis on recent observations as the weights become exponentially smaller with time. Smoothing methods are popular because they are fast (not a lot of computations are required) and relatively reliable when it comes to forecasts:

Simple exponential smoothing: The most basic model is called Simple Exponential Smoothing (SES). This class of models is most apt for cases when the considered time series does not exhibit any trend or seasonality. They also work well with series with only a few data points.

The model is parameterized by a smoothing parameter α with values between 0 and 1. The higher the value, the more weight is put to recent observations. When α = 0, the forecasts for the future are equal to the average of historical data (the one that the model was fitted to). When α = 1, all the forecasts have the same value as the last observation in the training data.

Simple Exponential Smoothing's forecast function is flat, that is, all the forecasts, regardless of the time horizon, are equal to the same value—the last level component. That is why this method is only suitable for series with neither trend nor seasonality.

Holt's linear trend method: Holt's model is an extension of SES that accounts for a trend in the series by adding the trend component into the model specification. This model should be used when there is a trend in the data, but no seasonality.

One issue with Holt's model is that the trend is constant in the future, which means that it increases/decreases indefinitely. That is why an extension of the model dampens the trend by adding the dampening parameter, φ. It makes the trend converge to a constant value in the future, effectively flattening it. Hyndman and Athanasopoulos (2018) state that φ is rarely smaller than 0.8, as the dampening has a very strong effect for smaller values of φ.

The best practice is to restrict the values of φ so that they lie between 0.8 and 0.98, because for φ = 1 the damped model is equivalent to the model without dampening.

In this recipe, we show you how to apply smoothing methods to Google's monthly stock prices (non-stationary data with a trend and no visible seasonality). We fit the model to the prices from 2010-2017 and make forecasts for 2018.