| Summary: | A new methodology for the missing-value completion of an incomplete nonstationary time series of a certain structure is presented and applied to measured data. The method is based on the modelling of long-term time series of wave data as a nonstationary stochastic process with yearly-long periodic mean value and standard deviation (periodically correlated stochastic process), introduced by the authors (Athanassoulis and Stefanakos, 1995). After a detrending and seasonal standardization, a low-order ARMA model is fitted to the (incomplete) residual stationary series using appropriate estimation techniques. The raw spectrum, calculated as the Fourier transform of a consistent estimate of the corresponding autocovariance function, is used for the estimation of the ARMA coefficients and the variance of the residuals. The incomplete time series of uncorrelated residuals is then completed by means of simulated data with the same first-order probability structure, and used, along with the ARMA model and the estimated deterministic components, to construct a new time series of the same structure without missing values. The above procedure is applied to two measured time series with different percentage of missing values. Comparisons of various statistical characteristics of the initial (incomplete) and reconstructed (completed) time series are satisfactory.
|
|---|