Modeling non-stationary extreme waves using a point process approach and wavelets

In the present paper a statistical model for extreme value analysis is developed, considering seasonality. The model is applied to significant wave height data from the N. Aegean Sea. To build this model, a non-stationary point process is used, which incorporates apart from a time varying threshold and harmonic functions with a period of one year, a component mu (w)(t) estimated through the wavelet transform. The wavelet transform has a dual role in the present study. It detects the significant "periodicities" of the signal by means of the wavelet global and scale-averaged power spectra and then is used to reconstruct the part of the time series, mu (w)(t), represented by these significant features. A number of candidate models, which incorporate mu (w)(t) in their location and scale parameters are tried. To avoid overparameterisation, an automatic model selection procedure based on the Akaike information criterion is carried out. The best obtained model is graphically evaluated by means of diagnostic plots. Finally, "aggregated" return levels with return periods of 20, 50 and 100 years, as well as time-dependent quantiles are estimated, combining the results of the wavelet analysis and the Poisson process model, identifying a significant reduction in return level estimation uncertainty, compared to more simple non-stationary models.