Reducing the effect of the autoreggressive term

[Ratskdup]

Hi all,
I am wondering if anyone has encountered an issue with dominated autoreggressive term. eg
Y(t) = intercept + a * Y(t-1) + b1*X1(t) + b2*X2(t)
where a >> b1 and b2, when values of Y(t-1) are comparable to those in X1(t) and X2(t), or
where a * Y(t-1) >> b1 * X1(t) and b2 * X2(t)

Is there a way in RATs we can reduce the effect of the Autoreggressive term?

Thx!

[TomDoan]

Do you have a reference on that? First, it's not clear why that would be "reducing" the effect of the autoregressive term, since the condition puts a lower bound on the AR term, not an upper bound. Also, how do you define >> operationally?

[Ratskdup]

Hi, thank you for getting back to me. I found a way to get around the problem. .. though have not solved the problem

Here is my question.... say we have the following AR(1) model:
home sales change (t) = 0.992 home sales change (t-1) + 0.002 GDP change (t), and assume both home sales and GDP changes are within -6% to +6%
then, since the term 0.992 * home sales change is a lot bigger in value (vs 0.002 * GDP change), it dominates and the 0.002* GDP change term has little effect on the model.
is there a way to constrain the coefficient of the home sales change (t-1) autoregressive term so that other exogenous variables can show up "stronger"?

[TomDoan]

For an ARDL model, the coefficient on the explanatory variable itself doesn't really determine the magnitude of the effect. Instead, in

y(t)=a*y(t-1)+bx(t)

the long-run effect of x is b/(1-a), so if a is close to 1, this could be quite large even if b is apparently small.