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

Author

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

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.

Suggested Citation

  • Moor, A. & La Vecchia, D. & Ronchetti, E., 2025. "On the use of the cumulant generating function for inference on time series," Computational Statistics & Data Analysis, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:csdana:v:201:y:2025:i:c:s0167947324001282
    DOI: 10.1016/j.csda.2024.108044
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