”Semi Parametric Estimation of Long Memory: the Holy Grail or a Poisoned Chalice?”

Considerable previous literature has addressed the problem of finding the most desirable estimator of the long memory parameter in a univariate time series. This paper considers three different estimation procedures: (i) the long memory parameter is obtained from a semi parametric Local Whittle estimator, which is used to filter the series before estimation of the short run parameters, (ii) a time domain MLE to jointly estimate parameters and (iii) the long memory and short memory structure is approximated by a high order linear autoregression. This paper examines the properties of estimated impulse response weights and finds that method (i) using the Local Whittle estimator is generally inferior to the other two methods. The high order AR approximation, ignoring the long memory dependency performs surprisingly well. The results cast doubt on the excessive research attention given to semi parametric estimation of the long memory parameter and suggest that MLE and even high order AR approximations are superior alternative procedures.