Time Series - 16 Method of Moving Averages - Even period cycle - Centred Moving Average
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- Опубликовано: 27 окт 2024
- #Statistics #Time #Series #Business #Forecasting #Moving #Average #Weighted #Centered #Trend #Values #Even
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
Find out 4 years’ centred moving averages.
Year 1 2 3 4 5 6 7 8 9 10
Value 430 470 450 460 480 470 470 500 490 480
Time Series, Business Forecasting, Method of Moving Averages, Centred Moving Average, Trend Value, Statistics, MBA, MCA, BE, CA, CS, CWA, CMA, CPA, CFA, BBA, BCom, MCom, BTech, MTech, CAIIB, FIII, Graduation,Post Graduation, BSc, MSc, BA, MA, Diploma, Production, Finance, Management, Commerce, Engineering , Grade-11, Grade- 12
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Very well explained! Greeting from Cambridge
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Thanks for explaining the "no man's land " concept and how we need to divide it by 2.(that was my doubt) Thank you sir.
Thankyou sir,it was really helpful
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Sir Tq Nice Explanation
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Perfect Sir
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it's very helpful
Add in four, add in pair, Trend or moving average ( divide by 8), If additive model (data- trend) if multiplicative model ( data/trend)
Thanks sir
nice explanation ,
there is another way...we don't need the 4 yearly moving avg column, we can just skip that column and just find 4 yearly and 2 yearly moving trend and atlast while calculating trend values divide the 2 yearly moving avg with 8 ....that's it...we get the same answer :)
Yes, but while teaching I always keep those students in my mind who are going to learn the topic first time or who are facing problem(s) in understanding even after trying to learn the same in their classroom or elsewhere. I prefer to explain not merely the solution of a problem just to arrive at the answer by any means. I want they understand the thing thoroughly at least by one way, which I suggest, first and then go for solving the same problem in other ways in their own. And, as far as examinations are concerned, still most of the teacher gives full marks for a solution only if the students write all the steps, mostly those steps which have been shown/discussed in the textbook or the suggested reference books... :)
Can you please list out its merits and demerits
great xplanation
Thanks
thanks alot sir it was helpful
Thank you
Ty sir
Is the same method used for 3 period moving averages?
No... I have discussed everything in different lectures taking different relevant examples/cases/problems...
In the title 'Time Series - 16', 16 indicates that this is lecture number 16 on Time Series and, so, there must be other 15 lectures before this lecture and few after this lecture... :)
thank you sir
Sir what to do with the missing values
Why in some cases we devide by 8 ?
... because they are summations of two different summations of 4...
thank u sir :)
plz answer the last statement in case of 6
thx
Sir kya aap bba sem 3rd nd 4th ki book quantitative methods ke all chapters ke sums ke tarike bata sakte hai (vnsgu) ke syllabus ki book ke sums plzzz....uske videos upload kijiye plz
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Tq sir
but plz give more example
There is a whole playlist on this and also many playlists on other topics/chapters on my channel...
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Plz hindi
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