TIME SERIES — Statistics STD 12 Commerce — Question
Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsTIME SERIES3 Marks
Question
Describe the method of moving average to find trend.
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Answer
The method of moving average is very useful to find trend by eliminating the effect of short-term variations.
$\rightarrow$ The period of moving average : The short-term variation are usually regular and have repetition. The period of repetition of these variations can be found by observing the given time series. The average is found from the number of observations corresponding to this period which is known as the period of moving average.
$\rightarrow$ Since the average value lie in the centre, the values obtained by this method show the trend.
$\rightarrow$ Suppose the values of variable are $y_1, y_2, …. y_n$ corresponding to time $t = 1, 2, …, n$ and the period of moving average is $3$ years. Then the mean of first three observations $y_1, y_2, y_3$ is found as $\frac{y_1+y_2+y_3}{3}$ and it is written against the centre of these three observations which is $y_2$. Further, the mean of successive three observation $y_2, y_3, y_4$ is obtained and it written against $y_3$. Similarly, finding successive moving total of three observations, averages are calculated. These average are called three yearly moving averages which indicate trend.
$\rightarrow$ The period of moving average not necessarily every time is year. It may be $5$ days, $4$ weeks, $7$ months, etc.
$\rightarrow$ If time period of moving average is an even number say. $4, 6, …$ etc., then the process of finding moving average is to be done twice.
$\rightarrow$ Suppose, the period of moving average is $4$ years. The four yearly successive averages
$\frac{y_1+y_2+y_3+y_4}{4}, \frac{y_2+y_3+y_4+y_5}{4}, \frac{y_3+y_4+y_5+y_6}{4}$
are written between $y_2$ and $y_3, y_3$ and $y_4, y_4$ and $y_5 ….$ respectively since, these averages are in between two years, the average of each pair of averages is found and written between two moving average. Thus, the average of the first two averages will be written against $y_3$. The averages thus obtained are called as four yearly moving average.
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