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relationship between AR(1) and MA(1)
Posted: Sat Nov 24, 2007 8:53 pm
by panta_rhei
Hi,
is it that the error term of an AR(1) process is an MA(1) process?
thanks in advance!
relationship between AR(1) and MA(1)
Posted: Sat Nov 24, 2007 9:18 pm
by meteor
No, the error term from an AR(1) process is white noise.
The process you mesntioned is an ARMA(1,1).
The only relationship I can think of: AR(1)=Ma(infinity); MA(1)=AR(infitnity) (provided the process is invertible).
A good reference about time series : Brockwell and Davis
relationship between AR(1) and MA(1)
Posted: Sun Nov 25, 2007 4:32 pm
by panta_rhei
hi, thanks for the reply.
but couldn't you rewrite the ar(1): Y_t=b*Y_t-1 + e_t into e_t=Y_t-b*Y_t-1 which is kind of a ma(1) ?
relationship between AR(1) and MA(1)
Posted: Sun Nov 25, 2007 10:45 pm
by meteor
I see your point but... the problem is that e_t is unobserved (and Y_t is)
So suppose that you want to estimate (the paramters of ) the second equation how do you gonna do? You will rewrite this equation into the first one.
So your first equation make more sense than the second one.
relationship between AR(1) and MA(1)
Posted: Fri Nov 30, 2007 5:56 pm
by functor
Except for MA(1), the 'random shocks' are supposed to be uncorrelated, but Y_t and Y_{t-1} are correlated since they come from an AR(1). They are not even martingale differences, as E[ Y_t | Y_{t-1}, .. Y_1 ] is not zero.