Forecasting with Missing Data: Application to Coastal Wave Heights

This paper presents a comparative analysis of linear and mixed models for short-term forecasting of a real data series with a high percentage of missing data. Data are the series of significant wave heights registered at regular periods of three hours by a buoy placed in the Bay of Biscay. The series is interpolated with a linear predictor which minimizes the forecast mean square error. The linear models are seasonal ARIMA models and the mixed models have a linear component and a non-linear seasonal component. The non-linear component is estimated by a non-parametric regression of data versus time. Short-term forecasts, no more than two days ahead, are of interest because they can be used by the port authorities to notify the fleet. Several models are fitted and compared by their forecasting behaviour.