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Stock prices are formed based on short and/or long-term commercial and trading activities that reflect different frequencies of trading patterns. However, these patterns are often elusive as they are affected by many uncertain political-economic factors in the real world, such as corporate performances, government policies, and even breaking news circulated across markets. Moreover, time series of stock prices are non-stationary and non-linear, making the prediction of future price trends much challenging. To address them, we propose a novel State Frequency Memory (SFM) recurrent network to capture the multi-frequency trading patterns from past market data to make long and short term predictions over time. Inspired by Discrete Fourier Transform (DFT), the SFM decomposes the hidden states of memory cells into multiple frequency components, each of which models a particular frequency of latent trading …