The holt’s exponential smoothing technique forecasts based on the level and trend of a time series. In this segment, you will learn about ‘Holt Winters’ Exponential Smoothing technique which forecasts based on level, trend and seasonality of a time series. Let’s hear from Chiranjoy as he explains how to capture the seasonality using the Holt Winters exponential smoothing.

In this video, you learnt that the forecast equation now has seasonal components, including level and trend i.e.

$$y_{t+1}=l_t+b_t+S_{t+1-m}$$

Here, m is the number of times a season repeats during a period. The seasonal component is calculated using the following equation:

Where γ is the weight assigned to the seasonal component of the recent observations. Note that the term yt−lt−1−bt−1 is the best guess of the seasonal component of the recent observation that is obtained after subtracting the level and the trend components from yt. The weight of γ is assigned to this component, whereas 1-γ is the weight assigned to the seasonal component of the recent observations.

The trend and the level equations respectively are as follows:

Note that in the video given above, Chiranjoy mentioned two methods of performing the Holt Winters’ smoothing techniques: additive and multiplicative methods. In a time-series data, if the seasonality is not a function of the level component or the difference between subsequent troughs of the time series data does not increase as you progress in the graph, then the Holt Winters’ additive method works best. You used this method for the quarterly ice cream sales example because as you can observe in the image below, the difference between the troughs does not increase.

But suppose seasonality is a function of the level and the difference between the troughs of the time series data increases as you progress in the graph, then you use the multiplicative method.

Recall the quarterly ice cream sales example where we were trying to capture the seasonality as well. Let us look at the demonstration again.

In this video, you understood that the Holt Winters’ smoothing method could capture the level and the trend along with the seasonality of the sales data of ice cream. You learnt how to calculate the values for each level, trend, seasonality and forecast considering the values of alpha, beta and gamma to be 0.2 each.