# Decomposition: Splitting Random Cyclical Variation

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• #47637

sophos9
Member

HiCan anyone provide any information on how once you have split out trend and seasonality, you can separate random and cyclical variation?I’ve read through the relevant chapters in the Book of Applied Statistics and this states there is no way to do it in Minitab.Any pointers?Cheers

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#159049

sophos9
Member

Sorry to ‘bump’ this up…. Can anyone provide any assistance to the above please?

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#159105

sophos9
Member

Is this an easy question that I’m missing the point or more complex?

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#159430

Kumar
Participant

I think it’s more a common sense to figure out the difference between the two by going through the relevant statistical charts…
random occurs randomly as its name suggest
cyclic – you can see a pattern in the chart

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#159432

sophos9
Member

Hi and thanks for the reply.Once you had de-trended and de-seasonalised the data set, it leaves cyclical variation and random noise. cyclical variation could happen over a number of years (8 in this case). I’ve been playing around with charting as well as researching what equations can be used to split out these 2 elements.The problem in this case is that the cyclical variation is less than the random noise and as such, is not identified in charts. My objective is to split out cyclical variation just to purely focus on random noise…

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#159433

Ashman
Member

Have you considered using Minitab’s Time Series Decomposition tool  to identify cyclic and random variation?

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#159434

sophos9
Member

Steve, HiYep, decomposition only separates seasonality and trend via multiplicative or additive models, it treats cyclical variation and random noise as the same thing. I’ve looked through the book of applied statistics which confirms that there is a manual calculation (not covered in Minitab) however I cannot find it anywhere….

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#159438

Larry
Participant

check out a book on forecasting such as the venerable Makridakis and Wheelwright and you will find several decomposition methods such as ratio to moving averages and Census II that will allow you to isolate cyclical factors (and you can do them the old fashioned way by hand instead of MTB button mashing).

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#159470

SB
Member

How many years of data are you using to detect this 8 year cycle?
Regards.

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#159481

BTDT
Participant

Sophos9:I like to use the partial autocorrelation function in MTB to identify significant seasonality when I am not sure of the length. Trending can also be diagnosed separately. Once identified, I build up an ARIMA model – not for the faint of heart, but possible.Cheers, BTDT

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