On Sat, 12 Mar 2011, Allin Cottrell wrote:
On Sat, 12 Mar 2011, Henrique Andrade wrote:
> Em 12 de mar�o de 2011 Allin escreveu:
>
> On Sat, 12 Mar 2011, Henrique Andrade wrote:
> >
> > > *Y(t) = X(t-1) + e1(t); if z(t-d)>=tau*
> > > *Y(t) = X(t-1) + e2(t); if z(t-d)<tau*
> >
> > If it's a TVAR I _think_ it should look more like
> >
> > Y_t = D1 + B1(L)Y_t + I_t*(D2 + B2(L)Y_t) + U_t
> >
> > where I_t = 1 if z(t-d) >= tau, otherwise 0.
> >
>
> Dear Allin, I need that the errors (and variances) differ in each regime:
>
> Y_t = D1 + B1(L)Y_t + U1_t, if z(t-d) >= tau
> Y_t = D2 + B2(L)Y_t + U2_t, otherwise
It seems to me that the error variances will automatically differ
across the two regimes in the version I constructed. But I'm not
experienced with TVARs so maybe I'm missing something.
Sorry, that response was too spineless. The errors and their
variances do differ in the formulation I gave, provided the
threshold hypothesis is correct.
I wrote the TVAR as
Y_t = D1 + B1(L)Y_t + I_t*(D2 + B2(L)Y_t) + U_t
where I_t = 1 if z(t-d) >= tau, otherwise 0.
We may rewrite this as
regime 1: U1_t = Y_t - (D1 + B1(L)Y_t)
regime 2: U2_t = Y_t - (D1 + B1(L)Y_t) - (D2 + B2(L)Y_t)
If D2 is non-zero and/or B2 is non-zero, the errors clearly differ
in the two regimes.
Allin