Sparse Interval-valued Time Series Modeling with Machine Learning

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, 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 is diverging with the sample size. Monte Carlo simulations demonstrate the favorable finite sample properties of the proposed estimation. 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 forest and multilayer perceptron for interval-valued data. Our findings highlight the potential of machine learning techniques in interval-valued time series analysis, offering new insights for financial forecasting and portfolio management.