Reservoir computing: Enhanced forecasting of ARIMA time series using multi echo state networks with time series preprocessing techniques

Accurate forecasting of complex temporal data is essential in various fields, such as finance, weather prediction, and market analysis. Traditional ARIMA models, while effective, might struggle with noisy data and low autocorrelation. This thesis investigates the use of Reservoir Computing, particularly Echo State Networks (ESN), for forecasting synthetically generated ARIMA time series. More specifically we use a particular model of ESN, Multi Echo State Networks (MultiESN), which allows multi-layered architectures of the reservoir (hidden) cells.By generating ARIMA time series with specific parameters, we create a challenging forecasting scenario characterized by high level of noise and small autocorrelation. The research focuses on optimizing MultiESN architecture, including layers, number of nodes, spectral radius (ρ), and leaking rate (α). Additionally, advanced smoothing and denoising techniques are applied to enhance trend detection and reduce noise. Our findings demonstrate the potential of MultiESN in improving forecasting accuracy for noisy ARIMA time series. This study contributes to the integration of statistical and machine learning methods in time series forecasting, highlighting the effectiveness of MultiESN and the impact of various optimization strategies and denoising techniques.