P1.T2.Diebold, Ch8: MA(q) Process-Conditional Mean

[gargi.adhikari]

In Reference to P1.T2.Diebold, Ch8: MA(q) Process-Conditional Mean :-
The Conditional Mean for MA(1) is : ( Theta). E t-1
What is the Conditional Mean for MA(q) ..?

Thanks much

 

[QuantMan2318]

Hi @gargi.adhikari

I am not completely sure on this, members who are more mathematically inclined can add further:

E(y_t|ohm_t-1) = Theta*e_t-1 in a MA(1) process
E(y_t|ohm_t-Q) = E(e_t + theta1 *e_t-1 + theta2*e_t-2 + .........thetaQ*e_t-Q | ohm_t-Q)

= E(e_t|ohm_t-Q) + theta1*E(e_t-1|ohm_t-Q) + ..............thetaQ*E(e_t-Q|ohm_t-Q)

= thetaQ * e_t-Q

Hope this is right

 

[gargi.adhikari]

@QuantMan2318 Thanks so much - I had messed up the expanded formula a bit and was getting to the same formula for the MA(1) ..but this helped me see where I went wrong !! Thanks so much !!