Conclusions from Monte Carlo

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Conclusions from Monte Carlo

• The constants in the linear and non linear
  autoregressive polynomials are estimated very
  accurately.
• Local Whittle estimator of d is superior in terms
  of bias to the MLE. However, the Local Whittle
  estimator has considerably higher variance than
  the MLE across all experiments.
• One-step MLE is generally superior in terms of
  both bias and variance for all the other
  parameters. Cautions against using Local Whittle
  estimator to fractionally filter the series
  before estimating the remaining parameters.
• The estimates of g are generally poor for all
  designs. The quality of the estimator improves
  with increasing degrees of persistence in the AR
  processes and also with increasing sample sizes.
• The parameter which is associated with the degree
  of persistence in the linear autoregressive
  processes is generally estimated with a downward
  bias, while the parameter which represents with
  the degree of persistence in the non-linear
  autoregressive processes is estimated with an
  upward bias across experiments. Total persistence
  is extremely well estimated.
• The value of d does not appear to be related to
  the quality of any of the MLE parameter
  estimates, including d itself.

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