A note on Whittle's likelihood
A note on Whittle's likelihood
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DOI：
10.1080/03610910600880203
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发表时间：
2006-10-01
影响因子：
0.9
通讯作者：
Walker, Stephen G.
中科院分区：
文献类型：
--
作者：
Contreras-Cristan, Alberto;Gutierrez-Pena, Eduardo;Walker, Stephen G.
由Whittle引入的近似似然函数已被用于估计各种时间序列模型的谱密度和某些参数。在这篇文章中，我们试图从经验上量化惠特尔方法在非标准环境中的效率损失。最近开发的一个代表性的一些一阶非高斯平稳自回归过程允许直接比较真实的似然函数与惠特尔。结论是，惠特尔的可能性可以产生不可靠的估计，在非高斯的情况下，即使是中等样本量。此外，对于小样本，如果过程的自相关性很高，惠特尔的近似是没有效率的，即使在高斯的情况下。虽然这些事实在一定程度上是已知的，但本研究揭示了在高斯和非高斯情况下，使用惠特尔的可能性所产生的效率损失的程度。
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.