An Extension of Temporal Feature Selection

Temporal Feature Selection (TFS) efficiently selects moving-average-based features for time-series prediction by combining prefix-sum computation with L1 regularization. However, conventional TFS is limited to linear combinations of moving averages and cannot directly incorporate higher-order polynomial features such as variance and covariance terms. In this study, we propose an extension of TFS that enables the inclusion of polynomial moving-average features up to a specified order. We formulate a unified feature space consisting of moving averages of polynomial terms and polynomial combinations of moving averages, and estimate their coefficients using Lasso regression. We further analyze alternative basis representations of candlestick data and demonstrate that the proposed \texttt{cdelta} representation yields more stable and informative features. Experiments on U.S. stock data (AAPL, MSFT, BAC) show that the proposed method achieves comparable or superior performance to technical-indicator-based Lasso models in terms of ROC--AUC and trading Sharpe ratio. Our results suggest that polynomial extensions of moving-average-based feature spaces provide a compact and effective framework for financial time-series prediction.