Title: Estimation and prediction in misspecified 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 misspecification of the short memory dynamics on estimation and prediction in a fractionally integrated model with an unknown mean. In particular, we derive the limiting distributions of three parametric estimators, namely, exact Whittle, time-domain maximum likelihood, and the conditional sum of squares (CSS), under common misspecification of the short memory dynamics. We also show 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. We further derive the properties of a linear predictor under misspecification. We show 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 Monte Carlo 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 misspecification designs. In terms of finite sample forecast performance, DWH also exhibits the smallest forecast error and mean squared forecast error.