In the last video, you learnt about the simple moving average technique. In this technique, we considered a window of past few observations whose average determined the forecast of the next observation.

In the simple moving average technique, we consider each observation in that window to equally influence the next value in the forecast. But intuitively, shouldn’t the most recent observations influence the next value more than past observations?

In the next video, you will learn more about this from Chiranjoy.

In this video, Chiranjoy explained a new technique called the weighted moving average technique. The underlying idea of this technique is that each observation influencing Yt+1 is assigned a specific weight. More recent observations get more weight, whereas the previous observations get less weight. Suppose you consider a time series data of 12 months and are forecasting yt+1. Then, the weighted moving average will be calculated as follows:

$$//mbox{\large$y$}\nolimits_t+1=\frac{a.y_1+b.y_2+c.y_3+……+k.y_t}{\begin{pmatrix}a+b+c+…..+&k\end{pmatrix}}//$$

such that a<b<c<…..k, where k is the largest weight assigned to the most recent data point i.e. y12.

Now, you know that time-series data primarily consists of the following three components:

- Level
- Trend
- Seasonality

As Chiranjoy mentioned, the family of weighted averages techniques, known as the exponential smoothing techniques, will help you capture each of the aforementioned three components one by one. In the next video, let’s first understand the simple exponential smoothing technique that helps us in capturing the level of time series data.

**Note: In the above video, at time 3:43, the equation should be α>α(1−α)>α(1−α)2….**

Let’s summarise the principles of the simple exponential smoothing technique. In this smoothing technique, the forecast observation data, Yt+1, is a function of the level component that is denoted by lt. Here, the level component is written as follows:

As Chiranjoy explained, the most recent value yt takes a weight of α, also known as the level smoothing parameter, whereas the previous observation’s level component takes the value of 1−α.

The values of α lie between 0 and 1. You can try to change the values of α such that for an optimum value of this level smoothing parameter the forecast fits well with the actual values and the subsequent values of the error terms are extremely low.

You will notice that each level term for yt,yt−1,yt−2 and so on can be written as follows:

Once you replace all the level terms in the forecast equation, you will obtain the following:

This technique is called a ‘simple exponential smoothing technique’.

Let’s now understand how to calculate the values of the level and the forecast using an example of the quarterly sales data of ice cream in a particular region. We will discuss the time series data for this problem first and then demonstrate how to calculate the forecast values using the simple exponential smoothing technique. After calculating the values, we will compare the forecast and the actual plots.

**Problem Statement:**

You have to forecast the sales of ice cream at a quarterly level using the simple exponential smoothing method. Chiranjoy will demonstrate how this forecast works step by step using a table using the value of

α

as 0.2 (weight).