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The root mean squared error

Given the data below on the Japanese yen to the dollar exchange rate. Each period is three months.
The spot rate is the actual exchange rate prevailing at the start of the period, while the Forward rate is the three-month forward exchange rate prevailing at the start of a period. The forecast rate is the forecast made by the Industrial Bank of Japan at the start of a period for the spot exchange rate at the start of the next period (That is, the forecast for three months later).
To illustrate, at the beginning of the third period, the actual spot exchange rate was 152.750, the three-month ahead forward rate was 153.600, and the rate forecast by the Industrial Bank for the start of the fourth period was 151. The actual spot exchange rate that was realized at the start of the fourth period was 149.400.
(a) Based on the root mean squared error, was the Industrial Bank of Japan able to outperform the forward rate (Hint, calculate the percentage forecast error)?
(b) You are informed that the spot rate realized three months after the last forecast given in the table below was 139.25. Hence, forecast the spot exchange rate.

Sample Solution

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