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Asymptotic distribution and subsampling in spectral analysis for spectrally correlated processes

Author

Listed:
  • Dudek, Anna E.
  • Majewski, Bartosz

Abstract

Spectrally correlated processes are harmonizable processes with spectral measures concentrated on a countable union of curves. Our study focuses on the spectral analysis of spectrally correlated processes, particularly in scenarios where these support curves take the form of lines with possible non-unit slopes. This subclass of spectrally correlated processes finds practical application, for example, in the problem of locating moving sources like aircraft, rockets, or other hostile jamming emitters emitting communication signals. Our research is focused on a frequency-smoothed periodogram along the support line as the spectral density function estimator. We derive its asymptotic distribution and based on that, we discuss the asymptotic properties of the introduced coherence estimator. Additionally, we formulate a consistent subsampling technique tailored for spectral analysis of spectrally correlated processes. We construct subsampling-based confidence intervals for spectral characteristics. Finally, we provide a numerical example illustrating a model relevant to applications in acoustics and communications.

Suggested Citation

  • Dudek, Anna E. & Majewski, Bartosz, 2026. "Asymptotic distribution and subsampling in spectral analysis for spectrally correlated processes," Stochastic Processes and their Applications, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:spapps:v:197:y:2026:i:c:s0304414926000633
    DOI: 10.1016/j.spa.2026.104931
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    References listed on IDEAS

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    1. Dehay, Dominique, 1994. "Spectral analysis of the covariance of the almost periodically correlated processes," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 315-330, April.
    2. Anna E. Dudek & Jacek Leśkow & Efstathios Paparoditis & Dimitris N. Politis, 2014. "A Generalized Block Bootstrap For Seasonal Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 89-114, March.
    3. Lei Shi & Shilpi Jain & Praveen Agarwal & Yousif Altayed & Shaher Momani, 2022. "Asymptotic Analysis About The Periodogram Of A General Class Of Time Series Models With Spectral Supportson Lines Not Parallel To The Main Diagonal," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-17, December.
    4. A. R. Soltani & A. R. Nematollahi & M. R. Mahmoudi, 2019. "On the asymptotic distribution of the periodograms for the discrete time harmonizable simple processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 307-322, July.
    5. A. Dudek, 2015. "Circular block bootstrap for coefficients of autocovariance function of almost periodically correlated time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 313-335, April.
    Full references (including those not matched with items on IDEAS)

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