Hybrid Time Series Forecasting with ARIMA, Echo State Networks, and LSTM

Recently, Echo State Networks (ESNs) have been applied to time series forecasting due to their computational efficiency and effectiveness on chaotic non-stationary time series data. However, their performance can be limited by instability in reservoir dynamics and sensitivity to hyperparameter selection. In this study, a novel hybrid model is proposed by combining Auto Regressive Integrated Moving Average (ARIMA), ESNs, and Long Short-Term Memory (LSTM) networks, with Discount Mean Square Forecast Error (DMSFE) applied for adaptive weighting. ARIMA is useful for modelling linear dependencies, while ESNs and LSTMs are effective for non-linear patterns. The proposed hybrid model achieves the best evaluation scores, outperforming every individual model and generating the best forecasts.