Estimation of fractional integration in the presence of data noise

A comparative study is presented regarding the performance of commonly used estimators of the fractional order of integration when data is contaminated by noise. In particular, measurement errors, additive outliers, temporary change outliers, and structural change outliers are addressed. It occurs that when the sample size is not too large, as is frequently the case for macroeconomic data, then non-persistent noise will generally bias the estimators of the memory parameter downwards. On the other hand, relatively more persistent noise like temporary change outliers and structural changes can have the opposite effect and thus bias the fractional parameter upwards. Surprisingly, with respect to the relative performance of the various estimators, the parametric conditional maximum likelihood estimator with modelling of the short run dynamics clearly outperforms the semiparametric estimators in the presence of noise that is not too persistent. However, when a non-zero mean is allowed for, it may reverse the conclusion.