Regularized Interval-Valued Time Series Modeling

By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance estimation method, which covers point-based estimators are special cases. We establish the consistency and oracle properties of the proposed penalized estimator, regardless of whether the number of predictors grows slower or faster than the sample size. Monte Carlo simulations demonstrate the favorable finite sample properties of the proposed estimator. Empirical applications to interval-valued crude oil price forecasting and sparse index-tracking portfolio construction illustrate the robustness and effectiveness of our method against competing approaches, including random forests and multilayer perceptrons for interval-valued data. Our findings highlight the potential of regularized techniques in interval-valued time series analysis, offering new insights for financial forecasting and portfolio management.