Q1

Simulate an AR(1) process (you pick the parameter value) of length 30. To this simulated series, fit AR models of order 0 through 6. Which model has the smallest AIC?

Repeat the simulation 500 times, how often is the model with the lowest AIC the true model?

Repeat again with a longer time series, do things change?

Repeat with a different parameter value, do things change?

Q2

1. Find and fit an ARIMA model to the deere2 dataset:

    library(TSA)
    data(deere2)
    ?deere2
   

2. Find and fit an ARIMA model to the robot dataset:

    library(TSA)
    data(robot)
    ?robot
   

You should include:

• how you chose the degrees of differencing d
• how you chose p, q
• diagnostics of your model fit
• the estimates and standard errors of your model parameters