6.
Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis 6.4.2. What are Moving Average or Smoothing Techniques?


Taking a moving average is a smoothing process 
An alternative way to summarize the past data is to compute the
mean of successive smaller sets of numbers of past data as follows.
Recall the set of numbers 9, 8, 9, 12, 9, 12, 11, 7, 13, 9, 11, 10 which were the dollar amount of 12 suppliers selected at random. Let us set \(M\), the size of the "smaller set" equal to 3. Then the average of the first 3 numbers is: (9 + 8 + 9) / 3 = 8.667.This is called "smoothing" (i.e., some form of averaging). This smoothing process is continued by advancing one period and calculating the next average of three numbers, dropping the first number. 

Moving average example 
The next table summarizes the process, which is referred to as
Moving Averaging. The general expression for the moving
average is
$$ M_t = \frac{X_t + X_{t1} + \cdots + X_{tN+1}}{N} \, . $$
The MSE = 2.42 as compared to 3 in the previous case. 