AR(4) vs SAR(4)

[rodo]

Hi, first of all, it is a great idea to have created this forum ! this was missing and will undoubtedly be of a great help for all of us.

My question: what difference between the AR(4) and SAR(4) components ? I didn't find a clear answer in the manual.

Thanks.

[EViews Gareth]

Mathematically you can represent an AR(1) term as:

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(1-pL)ut


where L is the lag operator.

An AR(1) AR(2) representation is:

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(1-p1L - p2L^2)u


A seasonal AR term just adds another level to this. An AR(1), AR(2) SAR(1) can be represented as:

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(1-p1L - p2L^2)(1-sL)u


where S is the seaonal AR term.

Note that if you don't have an AR term, then applying an SAR term is exactly the same as applying an AR term. i.e. the equation

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y c x ar(1)


is exactly the same as

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y c x sar(1)


I guess you can think of SAR terms as giving you the ability to apply an AR to an AR.

Hopefully someone who's a bit better at explaining Time Series can chime in with a better explanation in words.

[rodo]

OK great, thanks !!

Note that if you don't have an AR term, then applying an SAR term is exactly the same as applying an AR term. i.e. the equation

That is the key !