Moving averages

Sometimes the irregular component in time series may be so large that it creates difficulties in interpretation of the time plot series. In such cases we reduce this problem by using moving averages. We can smooth any irregularities using moving averages, based on the idea that any large irregular component at any point will have a smaller effect if we average the point with its immediate neighbors. This procedure is called a simple centered point moving average.

Let be n observations in a time series. A smoothed series can be obtained by using a simple centered point moving averages

For instance, if we want to find 3-point moving averages, then solve

and find . If , then the first available data will be .

General in this case is

If we set , then a 5-point moving averages will be formed as

.

Example:

The following data show the sales over the past six years. Compute a simple centered 3-point moving averages to smooth data

Year	Sales

Solution:

Since we need to find 3-point moving averages then , and .

Then

Using formula above, we obtain

The original data and smoothed data are given below:

Year	Sales
		-- 2878.67 2950.67 --

	Figure 7.1

The original data and smoothed data are graphed in Figure 7.1.

Remark:

To use MINITAB menu follow the following instructions:

1. Select Stat>Time series>Moving averages

2. Enter time series variable (for example, C1)

3. Enter the moving average length

4. Click results and select summary table and results table

5. Click OK.

Дата добавления: 2015-08-05