Advances in the Detection and Characterization of Nonstationary Processes: An Application to Riometers
Spectral-correlation detectors are used to determine if a stochastic temporal process contains nonstationary components from both the classes of spectrally-correlated and generalized almost-cyclostationary processes. The established multitaper spectral-correlation detectors are derived using solely the like-taper, cross-frequency, rotational and reflectional correlations between the eignecoefficient variables for the discrete Fourier transform of the temporal process. While this assumption is reasonable for the null hypothesis of zero frequency-offset spectral correlation, it is shown in this work to be less reliable for an alternative hypothesis of nonzero frequency-offset spectral correlation. Novel spectral-correlation detectors are introduced which account for the cross-taper, frequency-offset correlations between the eigencoefficient variables as well as the total correlation between them. In the asymptotic limit of increasing record size, these detectors are invariant to linear transfer functions. The test power and the robustness of the asymptotic quantile estimates to the process finitedimensional distributions is explored. The voltage series of a relative ionospheric opacity meter is considered for analysis. This instrument is sensitive to opacity fluctuations in the ionospheric D-region, and so it is used to monitor and forecast space-weather conditions. Results suggest that a complex-Gaussian approximation for the eigencoefficient variables is accurate. In this work, novel theory is introduced to help justify this distributional behaviour. The theory reveals a class of processes which can be used to assess the model uncertainty of the different spectral-correlation detectors, but it does not provide convergence rates over the record size. Therefore, a simulation study has been carried out to determine possible record sizes for which holds the aforementioned complex-Gaussian behaviour. For the considered riometer voltage series, results of this simulation study suggest that a 54-day record length at 120-second sampling period might well be sufficient for the complex-Gaussian behaviour to hold. Throughout the analysis, interesting periodic components are found in the voltage process.