Kanchana Nadarajah (Monash)

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Kanchana Nadarajah

Statistics

A seminar by Kanchana Nadarajah from Monash University

Title: Mean correction in mis-specified fractionally integrated models

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. This paper contributes to this line of research by 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 the short run parameters and the process mean. The methodology is developed within the framework of fractionally integrated processes exhibiting long, short and intermediate memory. 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 Whittle estimators, regardless of whether the process mean is known or unknown. In order to estimate the mean, we consider two estimators, namely, the sample mean estimator and the best linear unbiased estimator (BLUE). Our results show that 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 both estimators of the unknown mean under correct specification as well as under mis-specification. Monte Carlo simulations are used to quantify the finite sample behaviour of the estimators of the long memory parameter when the mean is also estimated.

Start date:

11am Thursday, 20 Jun 2019

End date:

12pm Thursday, 20 Jun 2019

Venue:

CBE LT1

Presenter(s):

Kanchana Nadarajah

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