# Probability Distribution of Forecasts

1. Probability Distribution of Forecasts. Assume that the following regression model was applied to historical quarterly data:

et = a0 + a1INTt + a2INFt 1 + *t

where et = percentage change in the exchange rate of the Japanese yen in period t

INTt = average real interest rate differÂ¬ential (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

*t = error term

Assume that the regression coefficients were estimated as follows:

a0 = 0.0

a1 = 0.9

a2 = 0.8

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?

2. During the Asian crisis in 1998, there were rumors that China would weaken its currency (the yuan) against the U.S. dollar and many European currencies. This caused investors to sell stocks in Asian countries such as Japan, Taiwan, and Singapore. Offer an intuitive explanation for such an effect. What types of Asian firms would have been affected the most? ( Expected length of response 150 to 200 words).

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1. Probability Distribution of Forecasts. Assume that the following regression model was applied to historical quarterly data:

et = a0 + a1INTt + a2INFt 1 + *t

where et = percentage change in the exchange rate of the Japanese yen in period t

INTt = average real interest rate ...

#### Solution Summary

The probability distribution of forecasts are examined.