On the use of the cumulant generating function for inference on time series

A. Moor, D. La Vecchia and E. Ronchetti

Computational Statistics & Data Analysis, 2025, vol. 201, issue C

Abstract: Innovative inference procedures for analyzing time series data are introduced. The methodology covers density approximation and composite hypothesis testing based on Whittle's estimator, which is a widely applied M-estimator in the frequency domain. Its core feature involves the cumulant generating function of Whittle's score obtained using an approximated distribution of the periodogram ordinates. A testing algorithm not only significantly expands the applicability of the state-of-the-art saddlepoint test, but also maintains the numerical accuracy of the saddlepoint approximation. Connections are made with three other prevalent frequency domain techniques: the bootstrap, empirical likelihood, and exponential tilting. Numerical examples using both simulated and real data illustrate the advantages and accuracy of the saddlepoint methods.

Keywords: Importance sampling; Legendre transform; Nuisance parameters; Saddlepoint approximation; Short and long memory; Whittle's M-estimator (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:201:y:2025:i:c:s0167947324001282

DOI: 10.1016/j.csda.2024.108044

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