Assume that the following regression model was applied to historical quarterly data:
et = a0 + a1INTt + a2INFt-1 +µt
Where et = percentage change in the exchange rate of the Japanese yen in period t
INTt = average real interest rate differential (U.S. interest rate minus Japanese interest rate) over period t
INFt-1 = inflation differential (U.S. inflation rate minus Japanese inflation rate) in the previous period
a0, a1, a2 = regression coefficients
µt = error term
Assume that the regression coefficients were estimated as follows:
a0 = .0
a1 = .9
a2 = .8
Also assume that the inflation differential in the most recent period was 3 percent. The real interest rate differential in the upcoming period is forecasted as follows:
Interest Rate
Differential Probability
0% .............. 30%
1 ............... 60
2 ............... 10
If Stillwater, Inc., uses this information to forecast the Japanese yen’s exchange rate, what will be the probability distribution of the yen’s percentage change over the upcoming period?