Probability distribution of forecasts. Assume that the following regression model was applied to histori- cal quarterly data:
et ¼ a0 þ a1INTt þ a2INFt-1 þ mt
where
et ¼ percentage change in the exchange rate of the Japanese yen in period t
INTt ¼ average real interest rate differential (UK interest rate minus Japanese interest rate) over period t
INFt21 ¼ inflation differential (UK inflation rate minus Japanese inflation rate) in the previous period
a0, a1, a2 ¼ regression coefficients
mt ¼ error term.
Assume that the regression coefficients were esti- mated as follows:
a0 ¼ 0:0
a1 ¼ 0:9
a2 ¼ 0:8
Also assume that the inflation differential in the most recent period was 3%. 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 Ltd 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?