Title: Issues in the estimation of misspecified models of fractionally integrated processes
Authors: Kanchana Nadarajah - University of Sheffield (United Kingdom) [presenting]
Gael Martin - Monash University (Australia)
Donald Poskitt - Monash University (Australia)
Abstract: The aim is to provide a comprehensive set of new theoretical results on the impact of mis-specifying the short run dynamics in fractionally integrated processes. We show that four alternative parametric estimators - frequency domain maximum likelihood, Whittle, time domain maximum likelihood and conditional sum of squares - converge to the same pseudo-true value under common mis-specification, and that they possess a common asymptotic distribution. The results are derived assuming the true data generating mechanism is a fractional linear process driven by a martingale difference innovation. A completely general parametric specification for the short run dynamics of the estimated (mis-specified) fractional model is considered, and with long memory, short memory and antipersistence in both the model and the data generating mechanism accommodated. An existing line of research on mis-specification in fractional models is extended. It also complements a range of existing asymptotic results on estimation in correctly specified fractional models. Open problems in the area are the subject of the final discussion.