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Method of Moving Averages
Method of moving averages is a very simple and flexible method of measuring trend. It consists in obtaining a series of moving averages (arithmetic means) of successive overlapping groups or sections of the time series. The averaging process smoothens out fluctuations and the ups and downs in the given data.
The moving average of period ‘M’ is a series of successive averages (arithmetic means) of M overlapping values at a time, starting with first, second, third value and so on.
Thus, for a time series, values y1, y2, y3, y4,… for different time periods the moving averages (MA) values of period M are given below
1st M.A. = (y1 + y2 + … yM) / M
2nd M.A. = (y2 + y3 + … yM + 1) / M
3rd M.A. = (y3 + y4 + … yM + 2) / M
When period is odd
If the period ‘M’ of the moving average is odd, then the successive value of the moving averages are placed against the middle value of the corresponding time intervals.
When period is even
If the period ‘M’ of the moving average is even then there are two middle periods and the moving average values are placed in between the two middle periods of the time intervals it covers. In this case the moving average values will not co-inside with a period of the given time series and attempt is made to synchronize them with the original data by taking two periods average of moving average and placing them in between the corresponding time periods. This technique is called centering and the corresponding moving average values are called centered moving average.
Merits and Demerits of moving average Method
Merits
1) This method does not require any mathematical complexities and is quite simple to understand and use as compared with the principle of least squares method.
2) This method does not involve any element of subjectivity, since the choice of the period of moving average is determined by oscillatory movements in the data and not by the personal judgement of the investigation.
3) Unlike the method of trend fitting by the principle of least squares the moving average method is quite flexible in the sense that a few more observations may be added to the given data without affecting the trend values already obtained. The addition of some new observations will simply result in some more trend values at the end.
4) In addition to the measurement of trend, the method of moving averages is also useful for measurement of seasonal, cyclical and irregular fluctuations.
Limitations
1) An obvious limitation of this method is that we cannot obtain the trend values for all the given observations. We have to for go the trend values for some observations of both the extremes depending on the period of moving average.
2) Since the trend values obtained by the method of moving averages cannot be expressed by any functional relationship, this method cannot be used for forecasting or predicting future values which is the main objective of trend analysis.
3) The selection of the period of moving average is very important and is not easy to determine particularly when the time series does not exhibit cycles, which are regular in period.
4) In case of a non-linear trend, which is generally the case in most economic and business time series, the trend values given by the method of moving average are biased and they lie either above or below the true swipe of the data.
Case
For the following data prove that 4 years’ centred moving average is equivalent to 5 years’ weighted average with weights 1,2,2,2,1 respectively.
Year 1 2 3 4 5 6 7 8 9 10 11
Value 9 11 15 13 10 12 16 19 15 13 9
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