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


When computing a running moving average, placing the average in the middle time period makes sense 
In the previous example we computed
the average of the first 3 time periods and placed it next to
period 3. We could have placed the average in the middle of
the time interval of three periods, that is, next to period 2. This
works well with odd time periods, but not so good for even time
periods. So where would we place the first moving average when
M = 4?
Technically, the Moving Average would fall at t = 2.5, 3.5, ... To avoid this problem we smooth the MA's using M = 2. Thus we smooth the smoothed values! 

If we average an even number of terms, we need to smooth the smoothed values 
The following table shows the results using M = 4.


Final table 
This is the final table:


Double Moving Averages for a Linear Trend Process  
Moving averages are still not able to handle significant trends when forecasting 
Unfortunately, neither the mean of all data nor the moving average of
the most recent M values, when used as forecasts for the next
period, are able to cope with a significant trend.
There exists a variation on the MA procedure that often does a better job of handling trend. It is called Double Moving Averages for a Linear Trend Process. It calculates a second moving average from the original moving average, using the same value for M. As soon as both single and double moving averages are available, a computer routine uses these averages to compute a slope and intercept, and then forecasts one or more periods ahead. 