Abstract
In recent years, the application of machine learning approaches to time-series forecasting of climate dynamical phenomena has become increasingly active. It is known that applying a band-pass filter to a time-series data is a key to obtaining a high-quality data-driven model. Here, to obtain longer-term predictability of machine learning models, we introduce a new type of band-pass filter. It can be applied to realtime operational prediction workflows since it relies solely on past time series. We combine the filter with reservoir computing, which is a machine-learning technique that employs a data-driven dynamical system. As an application, we predict the multi-year dynamics of the El Ni\~{n}o-Southern Oscillation with the prediction horizon of 24 months using only past time series.