Fuzzy time series forecasting of nonstationary wind and wave data
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## Abstract

In this paper, the well-known Fuzzy Inference Systems (FIS) in combination with Adaptive Network-based Fuzzy Inference Systems (ANFIS) are coupled for the first time with a nonstationary time series modelling for an improved prediction of wind and wave parameters. The data set used consists of ten-year long three-hourly time series of significant wave height HS, peak wave period Tp and wind speed WS based on hindcasts of WAVEWATCH III model and GFS analysis winds. The field used covers the area [30W,40E]×[50N,78N]. The initial time series is first decomposed by means of the aforementioned nonstationary modelling into a seasonal mean value and a residual time series multiplied by a seasonal standard deviation. Then, the FIS/ANFIS models are applied to the stationary part only in order to calculate forecasts of future values. Using the nonstationary modelling, forecasts of the full time series are finally obtained. For comparison purposes, the FIS/ANFIS models are also applied to the initial nonstationary series. The performance of both forecasting procedures is assessed by means of well-known error measures. The methodology is applied to obtain (a) point-wise forecasts for a specific datapoint and (b) field-wise forecasts for the whole field of wave parameters. Especially, the latter is performed for the first time. The comparison of the error measures from the two approaches showed that the forecasts based on the proposed methodology outperform the ones using only FIS/ANFIS models.

## Keywords

• Fuzzy time series;
• Significant wave height;
• Peak wave period;
• Wind speed;
• Forecasting;
• Prediction error

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