Suppose you have been given two different ARIMA (1,0,0) fitted timeseries models of the variable Yt:

Model A: Y_t = 15.0 + 0.5Y_t-1 + ε_t

Model T: Y_t = 45.0 - 0.5Y_t-1 + ε_t

Where ε_t is a normally distributed error term with mean 0 and standard deviation equal to 1.

a. The final observation in the sample (time period 06) is Y₀₆ = 31. Determine forecasts for periods 07, 08, and 09 for both models.

b. Suppose you now find out that the actual Y₀₇ was equal to 33. Revise your forecasts for periods 08 and 09 to take the new information into account.

c. Based on the fitted time series and your two forecasts, which model (model A or model T) do you expect to exhibit smoother behavior? Explain your reasoning.