relationship between AR(1) and MA(1)

panta_rhei · Post by **panta_rhei** » Sat Nov 24, 2007 8:53 pm

Hi,

is it that the error term of an AR(1) process is an MA(1) process?

thanks in advance!

meteor · Post by **meteor** » Sat Nov 24, 2007 9:18 pm

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

panta_rhei · Post by **panta_rhei** » Sun Nov 25, 2007 4:32 pm

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) ?

meteor · Post by **meteor** » Sun Nov 25, 2007 10:45 pm

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.

functor · Post by **functor** » Fri Nov 30, 2007 5:56 pm

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.