MA estimation

[Mikhail]

In http://forums.eviews.com/viewtopic.php?f=7&t=465 Gareth explained the difference between "LS Y C AR(1)" and "LS Y C Y(-1)" estimates.
I have an analogous question about MA estimation.
Assume we have white noise E and MA(1)-process Y generated by Y=C*E(-1)+E with some constant C.
Why the following regressions
LS Y E(-1)
LS Y MA(1)
give different results?
The first one estimates C, while the second one estimates 1/C...

Thanks.

[EViews Gareth]

I'm not sure I follow. E is not observered, so how can regression 1 be calculated?

[Mikhail]

I assume that E is given. Say,

Code: Select all

series E=nrnd smpl @first @first+1 series Y=0 smpl @first+1 @last series Y=E-3*E(-1) smpl @all equation ma.ls Y MA(1) equation ma1.ls Y E(-1)

Then the estimated coefficient at MA(1) is -1/3, while the estimated coefficient at E(-1) is -3.

[startz]

If I remember correctly, an MA coefficient of 1/3 and 3 imply the same correlogram. Choosing the coefficient under 1.0 is just a convention.

[EViews Gareth]

They're two completely different models. The MA model has no knowledge about the E series. It does not assume that E is given. Which is why you will never see identical results.

See what happens when you set the MA coefficient to an absolute value <1.

Edit: Startz beat me to it.

[Mikhail]

startz, Gareth, could you explain this, please. May be some reference.
Does EViews among different representaions with the same correlogram choose invertible one?