Generalized Seasonal Block Bootstrap in frequency analysis of cyclostationary signals

• Generalized Seasonal Block Bootstrap is applied to Fourier coefficients of cyclostationary signal.
• Consistency of GSBB is shown.
• Bootstrap pointwise and simultaneous confidence intervals are constructed.
• Real data example is presented.
• Efficiency and robustness to noise of the considered method is checked in simulation study.

In this paper the Generalized Seasonal Block Bootstrap (GSBB) method is applied to the first and the second order characteristics of the cyclostationary (CS) signal. The new method for detection of the significant frequencies in the Fourier expansions of the mean and the autocovariance functions of CS processes is provided. The consistency of GSBB is shown. Finally, the bootstrap pointwise and simultaneous confidence intervals are constructed and hence hypothesis tests for the presence of the first and the second order cyclostationarity can be performed. The real data example is presented to show the possible applications of our results. Moreover, the simulation study was performed to check the efficiency and robustness to the noise of the considered method.