Simple exponential smoothing technique captures level of a time series. In this segment you will learn about Holt’s exponential smoothing technique which captures both level and trend of a time series in the forecast. Let’s hear more on this technique from Chiranjoy.

In this video, Chiranjoy explained that now, the forecast equation is a function of both level and trend, that is,

$$//\widehat{\mbox{\large$y$}\nolimits_t}+1=\mbox{\large$l$}\nolimits_t+\mbox{\large$b$}\nolimits_t//$$

Here lt is the level component, and bt is the trend component. Here, the trend component is calculated as follows:

Here β is the smoothing parameter for trend. In the second equation given above, the difference in the level components in the recent observation shows the trend of the recent value, which is assigned a weight of β , whereas the trend values of the previous observations are assigned a weight of 1−β .

The equation for the level component remains the same with minor addition of the previous value’s trend component in the calculation of the previous value’s level component.

In the next video, let’s look at how to calculate the level, the trend and the forecast for the values of both alpha and beta as 0.2 for the same quarterly ice cream sales example you saw in the previous segment.

#### Note:

In the above video, the calculation of the trend is done considering the difference in the actual values rather than lt−lt−1. This is because the trend is calculated based on the immediate change, or the immediate delta. The immediate significant delta is the 130-80 difference in the actual value rather than the difference in the level terms. Thus the SME takes that value.

However, for our airline passenger example, we will be using the difference in the levels as depicted in the equation.

In the above video, you understood that the forecast plot now captures the trend component along with the level component but still does not capture the seasonality component.

Now that you learnt about Holt’s Exponential Smoothing, in the next video, you will learn how to build the model on the air passenger traffic data to forecast for the future.

In the next video, you will calculate the RMSE and MAPE for the forecast of Holt’s Exponential Smoothing model on Air Passenger traffic dataset.

The Holt’s exponential smoothing model forecasts based on the level and trend of a time series. In the next segment, you will learn another model of an exponetial smoothing technique family which also captures seasonality of a time series.