If a time series is stationary, the moving average method or single exponential smoothing can be used to analyze it. If a time series data has a trend component, then double exponential smoothing with Holts method can be used. However, if the time series data contains a seasonal component, then the Triple Exponential Smoothing (Winters) method can be used to handle it.

This method is based on three smoothing equations, Stationary Component, Trend and Seasonal. Both Seasonal component and Trend can be additive or multiplicative.

Additive

The whole smoothing equation

Trend smoothing

Seasonal smoothing

Forecasted value

Multiplicative

The whole smoothing equation

Trend smoothing

Seasonal smoothing

Forecasted value

Where l is seasonal length (for example, amount of month, or quartile in a year), T is trend component, S is seasonal adjustment factor, and is forecasted value for m next period.

Starting value , and

The starting values for and can be obtained from regression equations which have actual variables as dependent variables and time variables as independent variables. This equation constant is a starting value estimation for and slope of regression coefficient is a starting value estimation for the trend component . Whereas the starting value for the seasonal component is calculated by using dummy-variable regression on detrended data (without trend).