AR term of dY

[TomL]

Hi,

I have managed to confuse myself regarding the AR term in EViews. I have read an earlier thread, but I just want to make sure that I've got this right.

Regression: D(LiborSpread) = Alpha + Beta1*D(CDS) + Beta2*LiquidityProxy + AR(1) + e

Is the AR(1) a lag of the difference of the dependent variable? I am confused because substituting AR(1) for D(Y(-1)) yields different results.

Thanks,

Tom

[EViews Gareth]

AR(1) is a lag of the error term.

i.e. in an equation of

Code: Select all

Y=A+BX+e

then

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e=Y-A-BX

and so with an AR term you get

Code: Select all

Y = A + BX + C*(Y(-1) - BX(-1))

[TomL]

Isn't the lag of the error term MA(1)? And the lag of the dependent variable AR(1)?

[startz]

Isn't the lag of the error term MA(1)? And the lag of the dependent variable AR(1)?

No. Let me repeat what Gareth said slightly differently. If we we have the EViews equation

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ls y x ar(1)

then the equations are
y=c(1)*x + e
e = c(2)*e(-1) + eta

Alternatively, one can write

(y-c(2)*y(-1)) = c(1)*(x-x(-1)) + eta

[TomL]

I'm even more confused now. I understand that AR-terms can be substituted by lags of the error term, but AR terms are still (by definition) lags of the dependent variable.
In my equation I have not taken the difference of the liquidity proxy, so by rewriting it you won't end up with (y-c(2)*y(-1)) = c(1)*(x-x(-1)) + eta.

This is from the topic "ARIMA vs MA with lagged dependent variable", which is basically the same question as I have.

This is what startz wrote:

"There's some confusion here. Any pure ARMA(p,q) model is the same in EViews whether specified with AR terms or lags of the dependent variable. (There can be very small coefficient differences due to numerical issues.) Perhaps you should post more specifically what you're trying."

My question is: is the AR term in EViews still valid if the estimation is written with difference operators? Equation: D(Y) C X AR(1)
Or would it only be correct if the equation was written like DY C X AR(1)? [note that the dependent variable is now DY and not D(Y)]

Thanks for the help guys,

Tom

[trubador]

You can easily write these two equations in EViews and estimate to see if they yield the same output...

[EViews Gareth]

When Startz wrote:

"There's some confusion here. Any pure ARMA(p,q) model is the same in EViews whether specified with AR terms or lags of the dependent variable.

He specifically mentioned a pure ARMA model. You have independent variables in your equation, so what he wrote doesn't apply. Since the error term is now a function of the X variables too, an AR model is now a function of both the lagged values of the dependent variable and the independent variable.

[TomL]

Thanks for the help. I've got my answer.