Issues in the Estimation of Mis-Specified Models of Fractionally Integrated Processes

K. Nadarajah (), Gael Martin and Donald Poskitt

No 18/14, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: In this paper we quantify the impact of model mis-specification on the properties of parameter estimators applied to fractionally integrated processes. We demonstrate the asymptotic equivalence of four alternative parametric methods: frequency domain maximum likelihood, Whittle estimation, time domain maximum likelihood and conditional sum of squares. We show that all four estimators converge to the same pseudo-true value and provide an analytical representation of their (common) asymptotic distribution. As well as providing theoretical insights, we explore the finite sample properties of the alternative estimators when used to fit mis-specified models. In particular we demonstrate that when the difference between the true and pseudo-true values of the long memory parameter is sufficiently large, a clear distinction between the frequency domain and time domain estimators can be observed - in terms of the accuracy with which the finite sample distributions replicate the common asymptotic distribution - with the time domain estimators exhibiting a closer match overall. Simulation experiments also demonstrate that the two time-domain estimators have the smallest bias and mean squared error as estimators of the pseudo-true value of the long memory parameter, with conditional sum of squares being the most accurate estimator overall and having a relative efficiency that is approximately double that of frequency domain maximum likelihood, across a range of mis-specification designs.

Keywords: nd phrases: bias; conditional sum of squares; frequency domain; long memory models; maximum likelihood; mean squared error; pseudo true parameter; time domain; Whittle. (search for similar items in EconPapers)
JEL-codes: C18 C22 C52 (search for similar items in EconPapers)
Pages: 36
Date: 2014
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Journal Article: Issues in the estimation of mis-specified models of fractionally integrated processes (2020)
Working Paper: Issues in the estimation of mis-specified models of fractionally integrated processes (2018)
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