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190CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCYUse the method of undetermined coefficients again to solve for theexchange rate under the new assumption about the fundamentals byconjecturing the solution to depend on f t and on the two possible driftparameters δ 0 and δ 1s t = π 1 f t + π 2 p 0t δ 0 + π 3 p 1t δ 1 . (6.40)The new information available to agents is the current period realizationof the fundamentals which evolves according to a random walk.Since the new information is not predictable, the conditional expectationof the next period probability at date t is the current probability,E t (p 0t+1 )=p 0t . 10 Using this information, advance time by one periodin (6.40) and take date-t expectations to getE t s t+1 = π 1 (f t + p 0t δ 0 + p 1t δ 1 )+π 2 p 0t δ 0 + π 3 p 1t δ 1= π 1 f t +(π 1 + π 2 )p 0t δ 0 +(π 1 + π 3 )p 1t δ 1 . (6.41)Substitute (6.40) and (6.41) into (6.33) to getπ 1 f t +π 2 p 0t δ 0 +π 3 p 1t δ 1 = γf t +ψπ 1 (p 0t δ 0 +p 1t δ 1 +f t )+ψπ 2 p 0t δ 0 +ψπ 3 p 1t δ 1 ,(6.42)and equate coefficients to obtain π 1 =1,π 2 = π 3 = λ. This gives thesolutions t = f t + λ(p 0t δ 0 + p 1t δ 1 ). (6.43)Now we want to calculate the forecast errors so that we can see howthey behave during the learning period. To do this, advance the timesubscript in (6.43) by one period to gets t+1 = f t+1 + λ(p 0t+1 δ 0 + p 1t+1 δ 1 ).and take time t expectations to getE t s t+1 = f t + p 0t δ 0 + p 1t δ 1 + λp 0t δ 0 + λp 1t δ 1= f t +(1+λ)(p 0t δ 0 + p 1t δ 1 ). (6.44)10 This claim is veriÞed in problem 6 at the end of the chapter.