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On Dynamic Multiplier

On Dynamic Multiplier. Dynamic Multiplier. ARMA( p , q ):  ( L ) y t =  ( L )  t (L)=  ( L )/  ( L ) Multiplier  y t+j /  t Easiest way is to transform into the MA( ¥ ) form. X t = (L)u t = (sum over j=0 to inf) j  t-j Pick up the j-th coefficient.

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On Dynamic Multiplier

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  1. On Dynamic Multiplier

  2. Dynamic Multiplier • ARMA(p,q): (L)yt= (L)t (L)= (L)/(L) • Multiplier yt+j/t • Easiest way is to transform into the MA(¥) form. Xt = (L)ut = (sum over j=0 to inf)jt-j Pick up the j-th coefficient. • Long-run effect is simply (1) (1) = (1) / (1) = (1+ 1+...+ q)/(1-1- ... - p)

  3. Companion form of AR(p) Model AR(p): AR(p) Companion form casted as AR(1):

  4. Use AR(1) companion form to transform AR(p) models Yt = F Yt-1 + vt yt+j/t=11jwhich is (1,1) element ofQj. • Other ways to obtain dynamic multipliers* • Characteristic roots (eigenvalues) of Q. • Lag operator

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