Financial time series are inherently challenged by issues such as non-linearity and non-stationarity, which become particularly problematic when designing models for multi-step forecasting. To tackle the challenges of long-term forecasting, market traders often analyze data across multiple time frames and combine the results, providing them with insights into short-term, medium-term, and long-term trends. Inspired by this approach, we propose a model for multi-step forecasting of financial time series that effectively handles non-linearity and provides long-term forecasts without complex modeling. Our proposed model is a distributed probabilistic adaptive learning method that utilizes diverse data in each node. However, integrating diverse data in distributed models is challenging because improper data combination can disrupt the network’s stability, and the data must be sufficiently aligned to ensure effective learning. To address this, we employ scale-space kernels, which are mathematically grounded and preserve the essential characteristics of the data. Moreover, the integration of these kernels into the distributed probabilistic adaptive learning network ensures the stability and convergence of the network under certain conditions. Experiments on Standard & Poor’s 500 (S&P 500) and Tehran Stock Exchange (TSE) data demonstrate the model’s superior accuracy and robustness, especially in extended forecasting horizons.

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