A unified methodology for the analysis, completion and simulation of nonstationary time series with missing values, with application to wave data

摘要

A new methodology for the analysis, missing-value completion and simulation of an incomplete nonstationary time series of wave data is presented and validated. The method is based on the nonstationary modeling of long-term time series developed by the authors (J. Geophys. Res. 100(1995) 16,149). The missing-value completion is performed at the level of the series of the uncorrelated residuals, obtained after having removed both any systematic trend (e.g. monotone and periodic components) and the correlation structure of the remaining stationary part. The incomplete time series of uncorrelated residuals is then completed by means of simulated data from a population with the same probability law. Combining then all estimated components, a new nonstationary time series without missing values is constructed. Any number of time series with the same statistical structure can be obtained by using different populations of uncorrelated residuals. The missing-value completion procedure is applied to an incomplete time series of significant wave height, and validated using two synthetic time series having the typical structure of many-year long time series of significant wave height. The missing-value patterns used for validation have been obtained from existing (measured) wave datasets with 16.5 and 33 percent missing values, respectively.