Monday 4 February 2019, 3.00PM to 4.00pm
Speaker(s): Kanchana Nadarajah, Monash University
Abstract: Data in the economic and financial spheres often exhibit dynamic patterns characterized by a long-lasting response to past shocks. The correct modelling of such long-range dependence is of paramount importance, both in the production of accurate forecasts over long-term horizons and in the isolation of long-run equilibrium relationships. While the convention in the area has been to adopt complete parametric specifications for the dynamics in the time series, semi-parametric approaches have also featured of late. In this context, it is of particular importance to produce inferences about the long run that are not reliant on the correct modelling of the short run or short memory dynamics. This paper contributes to this line of research by rigorously developing the asymptotic theory for quantifying the impact of mis-specification of short memory dynamics in the context of estimating the long memory parameter – the parameter controlling the long range dependence – and short run parameters and the process mean parameter. The methodology is developed within the framework of fractionally integrated processes, as introduced by Granger and Joyeux (1980, Journal of Time Series Analysis, 1, 15–29) and Hosking (1981, Biometrika, 68, 165–175). In particular, we establish the limiting behaviour of parametric estimators (time domain maximum likelihood, conditional sum of squares and exact Whittle) under mis-specification of short memory dynamics, while allowing the process mean to be unknown. We also show that the limiting distributions of the three parametric estimators are identical to those of the frequency domain maximum likelihood and discrete Whittleestimators, regardless of whether the process mean is known or unknown. In order to estimate the mean parameter, we consider two estimators, namely, the sample mean estimator and the best linear unbiased estimator (BLUE). We rigorously establish the asymptotic properties both under the mis-specification of short memory dynamics and under correct specification of the full model. In view of our results, the sample mean estimator is unaffected by model mis-specification. However, the limiting behaviour of BLUE is sensitive to mis-specification of the short-memory dynamics. We establish the consistency of the estimators under correct specification as well as under mis-specification. Monte Carlo simulations suggest that our asymptotic properties established in this paper are consistent with the finite sample behaviour of the estimators.
Location: A/EC202 Economics Staff Room - Econometrics Cluster Seminar
Admission: All welcome