<![CDATA[This study proposes an Adaptive Linear Regression (ALR) framework for dynamic trend detection in non-stationary time-series data through adaptive window optimization and statistical validation. Unlike conventional linear regression models that rely on fixed lookback windows, the proposed framework dynamically determines the optimal window size based on a coefficient of determination (R²) threshold, allowing the model to adapt to changing data characteristics while filtering noisy observations. The validated regression model is further enhanced by constructing dynamic statistical boundaries using the Z-score distribution of regression residuals, enabling adaptive identification of significant deviations from local trends without requiring manually tuned parameters. The proposed framework was evaluated using high-frequency cryptocurrency time-series data collected from 2020 to 2025, including BTC/USDT, ETH/USDT, and SOL/USDT, as representative non-stationary datasets with high volatility. Experimental results demonstrate that the proposed approach achieves more robust trend detection and superior predictive consistency than conventional fixed-window regression and widely used baseline methods. In addition, the adaptive framework exhibits improved risk-adjusted performance and lower maximum drawdown when applied to an algorithmic trading scenario, indicating its practical applicability for dynamic decision-support systems operating on volatile time-series data. Overall, the proposed ALR framework provides a statistically grounded, interpretable, and adaptive approach for modeling non-stationary time-series and offers a promising alternative for intelligent data-driven applications.]]>
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