using moving average method find trend values and short term
Nuctuations
a. 3-year moving average
b. 4-year moving average
c. 5- year moving average
Answers
Answer:
This method uses the concept of ironing out the fluctuations of the data by taking the means. It measures the trend by eliminating the changes or the variations by means of a moving average. The simplest of the mean used for the measurement of a trend is the arithmetic means (averages).
Moving Average
The moving average of a period (extent) m is a series of successive averages of m terms at a time. The data set used for calculating the average starts with first, second, third and etc. at a time and m data taken at a time.
In other words, the first average is the mean of the first m terms. The second average is the mean of the m terms starting from the second data up to (m + 1)th term. Similarly, the third average is the mean of the m terms from the third to (m + 2) th term and so on.
If the extent or the period, m is odd i.e., m is of the form (2k + 1), the moving average is placed against the mid-value of the time interval it covers, i.e., t = k + 1. On the other hand, if m is even i.e., m = 2k, it is placed between the two middle values of the time interval it covers, i.e., t = k and t = k + 1.
When the period of the moving average is even, then we need to synchronize the moving average with the original time period. It is done by centering the moving averages i.e., by taking the average of the two successive moving averages.
Drawbacks of Moving Average
The main problem is to determine the extent of the moving average which completely eliminates the oscillatory fluctuations.
This method assumes that the trend is linear but it is not always the case.
It does not provide the trend values for all the terms.
This method cannot be used for forecasting future trend which is the main objective of the time series analysis.
Solved Example for You
Problem: Calculate the 4-yearly and 5-yearly moving averages for the given data of the increase Ii in the population of a city for the 12 years. Make a graphic representation of it.
moving average
Solution:
t Ii 5-yearly moving totals 5-yearly moving averages 4-yearly moving totals (not centered) 4-yearly moving average (not centered) 2-period moving total (centered) 4-yearly moving average (centered)
(1) (2) (3) (4) = (3) ÷ 5 (5) (6) = (5) ÷ 4 (7) (8) = (7) ÷ 2
1 100
2 100
400 100
3 100 500 100 200 100
400 100
4 100 475 95 193.75 96.875
375 93.75
5 100 450 90 181.25 90.625
350 87.50
6 75 470 94 180 90
370 92.50
7 75 490 98 190 95
390 97.50
8 120 510 102 206.25 103.125
435 108.75
9 120 555 111 228.75 114.375
480 120
10 120 600 120 240 120
480 120
11 120
12 120
Here, the 4-yearly moving averages are centered so as to make the moving average coincide with the original time period. It is done by dividing the 2-period moving totals by two i.e., by taking their average. The graphic representation of the moving averages for the above data set is
moving average
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Step-by-step explanation:
