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

6.4.2.2.

Centered Moving Average

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.

Interim Steps

Period	Value	MA	Centered
1	9
1.5
2	8
2.5		9.5
3	9		9.5
3.5		9.5
4	12		10.0
4.5		10.5
5	9		10.750
5.5		11.0
6	12
6.5
7	11

Final table

This is the final table:

Period	Value	Centered MA
1	9
2	8
3	9	9.5
4	12	10.0
5	9	10.75
6	12
7	11

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.