Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing.

@article{Maraun2007NonstationaryGP,
  title={Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing.},
  author={D. Maraun and Juergen Kurths and Matthias Holschneider},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2007},
  volume={75 1 Pt 2},
  pages={016707}
}
We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an… CONTINUE READING
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