Small sample properties of the maximum likelihood estimator for low order ARFIMA models : a Monte Carlo simulation

Abstract EN

We analyze by simulation the properties of three estimators for low order autoregressive fractionally integrated moving average model (ARFIMA (p,d,q)).

The estimators considered are the exact maximum likelihood estimator, EMLE, the Modified maximum likelihood estimator, MMLE, and the Whittle maximum likelihood estimator, WMLE.

The length of the series is 100.

The estimators are compared in terms of pile-up effect, mean square error, and percentage confidence level. The WMLE turns out to be a reliable estimator for ARIMA (p,d,q), when d = 0 and ARFIMA models.

Its small losses in performance in case of “easy” models are compensated sufficiently in more “difficult” models.

The MMLE is an alternative to the WMLE but is computationally more demanding.

It is either equivalent to the EMLE or more favorable than EMLE.

The EMLE, on the other hand, should only be used with care for fractionally integrated models due to its potential large negative of the fractional integration parameter.

In general, one should proceed with caution for AR1MA (1,0,1) models writh almost canceling roots, and, in particular, in case of the EMLE, and the MMLE, for inference in the vicinity of a moving average root of+1.