A time series model has been fit and checked with historical data yielding
Yt = 50 + .45Yt-1 + εt
Suppose at time t = 60 the observation is Y60 = 57.
a. Determine forecasts for periods 61,62, and 63 from origin 60.
b. Suppose the observed value of Y61is 59. Update the forecasts for periods 62 and 63.
c. Suppose the estimate for the variance of the error term is s2 = 3.2. Compute a 95% prediction interval about the forecast for period 61.