Title: Estimation and prediction in mis-specified fractionally integrated models with an unknown mean Authors:  Kanchana Nadarajah - University of Sheffield (United Kingdom) [presenting]
Gael Martin - Monash University (Australia)
Indeewara Perera - University of Sheffield (United Kingdom)
Donald Poskitt - Monash University (Australia)
Abstract: The aim is to explore the impact of mis-specification of the short memory dynamics on estimation and prediction in a fractionally integrated model with an unknown mean. In particular, the limiting distributions of three parametric estimators, namely, exact Whittle, time-domain maximum likelihood, and the conditional sum of squares (CSS), are derived under common mis-specification of the short memory dynamics. It is also shown that, conditional on the use of a consistent estimator of the mean, these estimators converge to the same pseudo-true value and that their asymptotic distributions are identical to those of two alternative estimators that are mean invariant: the frequency domain maximum likelihood and discrete Whittle (DWH) estimators. Further, the properties of a linear predictor under misspecification are derived. It is shown that the linear predictor for zero-mean processes is biased, and the mean squared forecast error depends on the true and pseudo-true value of the fractional differencing parameter. A simulation study shows that the DWH estimator of the pseudo-true value of the fractional differencing parameter has the best overall performance in terms of bias and mean squared error in finite samples across a range of mis-specification designs. Regarding finite sample forecast performance, DWH exhibits the smallest forecast error and mean squared forecast error.