Nonstationary stochastic modelling of multivariate long-term wind and wave data

In the present work, a nonstationary stochastic model, which is suitable for the analysis and simulation of multivariate time series of wind and wave data, is being presented and validated. This model belongs to the class of periodically correlated stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic process). First. the time series is appropriately transformed to become Gaussian using the Box-Cox transformation. Then, the series is decomposed, using an appropriate seasonal standardization procedure, to a periodic (deterministic) mean value and a (stochastic) residual time series multiplied by a periodic (deterministic) standard deviation. The periodic components are estimated using appropriate time series of monthly data. The residual stochastic part, which is proved to be stationary, is modelled as a VARMA process. This way the initial process can be given the structure of a multivariate periodically correlated process. The present methodology permits a reliable reproduction of available information about wind and wave conditions, which is required for a number of applications.