Authors - Onkar Yende, Nayan Bhutada, Mohit Thakre, Sai Khadse, Mridula Korde Abstract -Reliable stock price forecasting remains challenging due to the noisy, nonlinear, and non-stationary characteristics of financial time-series data. Traditional statistical methods and deep learning models that rely solely on raw price data often struggle to capture short-term fluctuations and evolving market dynamics. To address these limitations, this study proposes a hybrid forecasting framework that integrates causal time-domain filtering, time–frequency feature extraction, and deep learning–based temporal modeling. The proposed approach employs Savitzky–Golay and Kalman filters to sup press high-frequency market noise while preserving important price trends in a causality-aware manner suitable for real-time forecasting. Localized spectral fea tures representing transient and time-varying market behavior are then extracted using the Short-Time Fourier Transform (STFT). These enhanced time-domain and frequency-domain features are combined and modeled using a Long Short Term Memory (LSTM) network, which effectively captures long-range depend encies and nonlinear temporal patterns in financial data. The framework is evaluated using standard performance metrics, including RMSE, MAPE, and R². Experimental results demonstrate that integrating causal filtering with STFT-based features significantly improves forecasting accuracy and robustness compared to baseline models, providing a reliable and practical solution for short-term and multi-step stock price prediction.
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