19 Probability distribution of forecasts. Assume that the following regression model was applied to
19 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 differen- tial 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?