Use R for this problem – except for part d.
- Simulate the following AR(2) process:
Yt = 1 – 0.3 *Yt-1- 0.1*Yt-2 + e t where e t ~iidN(0, 1)
Use 300 data points of the simulated data as your data set.
- Plot the data and the correlogram.
- Use the first 290 data points to estimate an AR(2) model. Present the estimated model.
- Using the estimated model derive optimal point forecasts and the corresponding 90% forecast intervals of y for t=291, 292, and 293.
- Now use R to generate forecasts of y for t=291-300 and the corresponding standard errors of forecasts. For the first three forecast periods, compare R results and your results in part d. Are they close?
- Again use R to plot your actual data and the forecasts to see how your forecast performed vis- a- vis the actual y in the forecast period.