Simulated data

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Use R for this problem – except for part d.

  1. 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.

  1. Plot the data and the correlogram.
  2. Use the first 290 data points to estimate an AR(2) model. Present the estimated model.
  3. Using the estimated model derive optimal point forecasts and the corresponding 90% forecast intervals of y for t=291, 292, and 293.
  4. 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?
  5. 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.

 

 

 

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