Contreras-Cristan, A. and Gutierrez-Pena, E. and Walker, S.G. (2006) A note on Whittle's likelihood. Communications in Statistics - Simulation and Computation, 35 (4). pp. 857-875. ISSN 0361-0918.
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The approximate likelihood function introduced by Whittle has been used to estimate the spectral density and certain parameters of a variety of time series models. In this note we attempt to empirically quantify the loss of efficiency of Whittle's method in nonstandard settings. A recently developed representation of some first-order non-Gaussian stationary autoregressive process allows a direct comparison of the true likelihood function with that of Whittle. The conclusion is that Whittle's likelihood can produce unreliable estimates in the non-Gaussian case, even for moderate sample sizes. Moreover, for small samples, and if the autocorrelation of the process is high, Whittle's approximation is not efficient even in the Gaussian case. While these facts are known to some extent, the present study sheds more light on the degree of efficiency loss incurred by using Whittle's likelihood, in both Gaussian and non-Gaussian cases.
|Uncontrolled keywords:||ARCH process; autocorrelation function; gamma process; Gaussian process; periodogram; spectral density; stationary time series|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics|
|Depositing User:||Judith Broom|
|Date Deposited:||05 Sep 2008 16:16|
|Last Modified:||14 Jan 2010 14:40|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/10523 (The current URI for this page, for reference purposes)|
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