Application of Empirical Mode Decomposition and Hodrick Prescot filter for the prediction single step and multistep significant wave height with LSTM

Abstract

The study discusses the application of the Empirical Model Decomposition (EMD) and Hodrick Prescot (HP) filter for significant wave height prediction. Long Short-Term Memory (LSTM) is applied for sequence predictions in Natural Language Processing (NLP). LSTM can also be modeled to time series forecasting, particularly for cyclic data since LSTM learns from experience to forecast the data. The time series signal is a combination of frequencies or spectra, when the LSTM is applied to the raw signal the prediction is lagged, to reduce the lag in the forecast the noise in the time series signal is filtered. Since, the time series consists of various frequency components, filtering the higher-frequency components is required to reduce the delay in prediction from the LSTM neural network model. The EMD is applied to the original time series wave data to split the signal into several frequencies in time series or Intrinsic Mode Functions (IMFs). Similarly, when the HP filter is applied to the original wave data or time series signal it gives a trend and cycle. The LSTM is applied to the IMFs and HP filter trend time series to predict the EMD-IMFs and Trend respectively. All the predicted IMFs are summed to compare with the original raw time series. The single step and multistep prediction or forecasting is carried out for 1-h interval, 6-h, 12-h, and 24 h interval. With the increase in forecasting interval the error values also increased and changing the lambda parameter of HP filter played a critical step for the multistep prediction. The EMD-LSTM is computationally expensive as it takes higher amount time to predict each IMF compared to HP-LSTM. Finally, the results are compared with between normal LSTM, EMD-LSTM and HP-LSTM.