Modeling Functional Time Series and Mixed-Type Predictors With Partially Functional Autoregressions
提出部分函数自回归模型，用二维系数算子捕捉曲线序列依赖，用双层正则化估计混合类型预测变量的个体和组效应，在德国天然气日流量数据中验证了预测精度和动态洞察。
In many business and economics studies, researchers have sought to measure the dynamic dependence of curves with high-dimensional mixed-type predictors. We propose a partially functional autoregressive model (pFAR) where the serial dependence of curves is controlled by coefficient operators that are defined on a two-dimensional surface, and the individual and group effects of mixed-type predictors are estimated with a two-layer regularization. We develop an efficient estimation with the proven asymptotic properties of consistency and sparsity. We show how to choose the sieve and tuning parameters in regularization based on a forward-looking criterion. In addition to the asymptotic properties, numerical validation suggests that the dependence structure is accurately detected. The implementation of the pFAR within a real-world analysis of dependence in German daily natural gas flow curves, with seven lagged curves and 85 scalar predictors, produces superior forecast accuracy and an insightful understanding of the dynamics of natural gas supply and demand for the municipal, industry, and border nodes, respectively.