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  1. 1. Repeat many times(1000 times in my case)
  2. 2. Generate $phi$ and $sigma^2$.
  3. 3. Repeat 100 times:
  4. 4. Simulate an AR1 series with parameters from 2.
  5. 5. Compute 95% confidence intervals for $phi$ and $sigma^2$.
  6. 6. Verify that 5% of the time the above CI does NOT contain
  7. the parameters generated in step 2(this is equivalent to the
  8. CI containing the parameter 95% of the time).
  9. 7. This amounts to saying that the distribution of number of
  10. time the CI does NOT contain the original parameter is
  11. Binomial(100,.05)
  12. We will finally get 1000 element vector which SHOULD be
  13. distributed as rbinom(n=1000,size=100,p=.05)
  14. I then do a qqplot of the observed vector with the expected vector.
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