A1025
Title: Mean correction and forecasting in mis-specified fractionally integrated models
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 impact of mis-specification of short memory dynamics on estimation and forecasting in a fractionally integrated model with an unknown mean is explored. 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 mis-specification of the short memory dynamics. We also show that these estimators converge to the same pseudo-true value and that their asymptotic distributions are identical to those of the frequency domain maximum likelihood and discrete Whittle (DWH) estimators. We further derived the properties of a linear predictor under mis-specification. For zero-mean processes, the linear predictor is still unbiased for the future value, but not the best predictor. In a Monte Carlo simulation study, we observe that the two time-domain estimators exhibit the smallest bias and mean squared error (MSE) as estimators of the pseudo-true value of the long memory parameter, with CSS being the most accurate estimator overall. When the mean is estimated from data, the DWH estimator is preferred in terms of bias and MSE. Furthermore, the linear predictor exhibits significant bias under mis-specification. In terms of finite sample forecast performance, CSS entails the best overall forecast error and mean squared forecast error when the mean is known, whereas the DWH exhibits the best performance when the mean is estimated.
