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Inference for Generalized Almost Cyclostationary Processes with Unknown Lag-Dependent Cycle Frequencies

  • Anna E. Dudek
  • Antonio Napolitano
  • Jakub Rutkowski
  • Jakub Wojdyła
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Abstract

In this paper, we study the estimation problem of generalized cyclic autocorrelation functions with unknown lag-dependent cycle frequencies for generalized almost cyclostationary processes. We establish the conditions under which the estimator is mean-square consistent and asymptotically normal. In addition, we consider the discrete-time counterpart of this estimator for sampled stochastic processes and establish the sufficient conditions for its mean-square consistency and asymptotic normality. A Monte Carlo study in a realistic simulation scenario illustrates the results: the correlogram with estimated frequencies behaves like the correlogram with the true frequencies.

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Cite

BibTeXRIS
BibTeX
@misc{dudek2026inference,
  title = {{Inference for Generalized Almost Cyclostationary Processes with Unknown Lag-Dependent Cycle Frequencies}},
  author = {Anna E. Dudek and Antonio Napolitano and Jakub Rutkowski and Jakub Wojdyła},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  url = {https://amu.hal.science/hal-05720542v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Inference for Generalized Almost Cyclostationary Processes with Unknown Lag-Dependent Cycle Frequencies
AU  - Anna E. Dudek
AU  - Antonio Napolitano
AU  - Jakub Rutkowski
AU  - Jakub Wojdyła
PY  - 2026
DA  - 2026/08/18
PB  - HAL
UR  - https://amu.hal.science/hal-05720542v2
AB  - In this paper, we study the estimation problem of generalized cyclic autocorrelation functions with unknown lag-dependent cycle frequencies for generalized almost cyclostationary processes. We establish the conditions under which the estimator is mean-square consistent and asymptotically normal. In addition, we consider the discrete-time counterpart of this estimator for sampled stochastic processes and establish the sufficient conditions for its mean-square consistency and asymptotic normality. A Monte Carlo study in a realistic simulation scenario illustrates the results: the correlogram with estimated frequencies behaves like the correlogram with the true frequencies.
ER  -