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Inference with the Whittle Likelihood: A Tractable Approach Using Estimating Functions
Author(s) -
Jesus Joao,
Chandler Richard E.
Publication year - 2017
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12225
Subject(s) - inference , estimator , mathematics , asymptotic distribution , sampling distribution , statistical inference , process (computing) , mathematical optimization , distribution (mathematics) , econometrics , statistics , computer science , artificial intelligence , mathematical analysis , operating system
The theoretical properties of the Whittle likelihood have been studied extensively for many different types of process. In applications however, the utility of the approach is limited by the fact that the asymptotic sampling distribution of the estimator typically depends on third‐order and fourth‐order properties of the process that may be difficult to obtain. In this article, we show how the methodology can be embedded in the standard framework of estimating functions, which allows the asymptotic distribution to be estimated empirically without calculating higher‐order spectra. We also demonstrate that some aspects of the inference, such as the calculation of confidence regions for the entire parameter vector, can be inaccurate but that a small adjustment, designed for application in situations where a mis‐specified likelihood is used for inference, can lead to marked improvements.