Recall that {xt} is a martingale ifE[xn+h

Recall that {x,} is a martingale if E[x,,+h Ix" ,xn_1, - - ' ]=x,, for all n and for all lead times I: >0. Actually, to establish that {x,} is a martingale, one simply needs to prove the above formula for h =1 since it can be shown that if it holds for h = 1 it must hold for all h >0. 1) Suppose x, =x,_1+, where 8, =6, +Be,_1e,_2, B0, and {e,} is strict white noise. a) What is the best linear predictor of xn+1 based on x\" ,xn_1 , ' . ' ? Justify your answer. b) What is the best possible predictor of xn+1 based on x\" ,xn_1 , - ' - ? Justify your answer. 0) Compare your answers to a) and b) to decide whether {x,} is a martingale. (Keep in mind the discussion at the top of this handout)