3. A time series model has been fit and checked with historical data yielding Suppose at time the observation is .

a. Determine forecasts for periods 61, 62, and 63 from origin 60.

b. Suppose the observed value of is 59. Update the forecasts for periods 62 and 63.

c. Suppose the estimate for the variance of the error term is . Compute a 95% prediction interval about the forecast for period 61.