This example shows comparison of single, double and triple exponential smoothing for a data set.

The following data set represents 24 observations. These are six years of quarterly data (each year has four quarters).

Actual Time Series with forecasts

The updating coefficients were chosen by a computer program such that the MSE for each of the methods was minimized.

**Example of the computation of the Initial Trend**

The data set consists of quarterly sales data. The season is 1 year and since there are 4 quarters per year, L=4. Using the formula we obtain:

**Example of the computation of the Initial Seasonal Indices**

In this example we used the full 6 years of data. Other schemes may use only 3, or some other number of years. There are also a number of ways to compute initial estimates.