Exponential Smoothing

The Exponential Smoothing command computes exponentially weighted averages and provides short-term forecasts for a time series.

# How To

Run the Statistics→Time Series → Exponential Smoothing command.

Select a variable with time series.

Select the exponential smoothing method and model - simple, Holt’s, Holt-Winters. (v6.5)

Optionally, in the Advanced Options, change the value of smoothing factor (default value: 0.1) and select a model with trend or seasonality.

Smoothing factor is also called damping factor. When is
close to 1, dampening is quick and when is
close to 0, dampening is slow. *Please note: default value of smoothing
factor in the Analysis Toolpak from the Microsoft Excel package is 0.3*.

# Results

Table with measures of accuracy (MAPE, MAD, MSD), table and chart with original and smoothed time series are generated.

### Single exponential smoothing

The simplest form of exponential smoothing is given by the formulas:

where
is
the smoothing factor, .

In other words, the smoothed statistic is
a simple weighted average of the previous observation and
the previous smoothed statistic .

### Measures of accuracy

**Mean absolute percentage error (MAPE)** –
measures the size of the error in percentage terms. For example, if the MAPE is
10, on average the forecast is off by 10%.

Mean absolute deviation (MAD) is the average of the absolute deviations from a mean. It measures accuracy in the data units.

Mean squared deviation (MSD) – measures the average of the squares of the errors. It is a more sensitive measure of an unusually large forecast error than MAD.