非平稳时间序列的非参数预测回归

In this proposal we propose three classes of predictive regression models: semiparametric predictive model, time-varying coefficient predictive model, and additive predictive model, which are motivated from real applications of testing predictability and stability of stock returns. It is well known that the asymptotic theory for standard nonparametric regression models has been well established under independent and weakly dependent settings. However, at the current stage, little is known regarding asymptotic theory for nonparametric predictive regression modeling due to the difficulties associated with endogeneity, nonstationarity,persistency and instability. To overcome these difficulties, this proposal provides a sound theoretical basis for modeling the aforementioned predictive regression models and extends the applications of the proposed modeling approaches to the nonstationary and nonlinear realm. From the theoretical perspective, this proposal will explore some new nonparametric modeling methods to handle persistent, nonstationary and nonlinear time series data and to provide the asymptotic results for the proposed nonparametric estimators. As expected, these theoretical results will be different from their counterparts for standard nonparametric regression models. Empirically, the applications of nonparametric predictive models would provide much more accurate and efficient forecasting results.

本项目提出三类预测回归模型：半参数预测模型，时变系数预测模型，及可加预测模型。这些模型提出的动机来自于股票收益率的稳定性和可预测性检验。大家已知标准非参数回归模型的渐进理论建立于独立或弱相关情形。然而，在当前情形下，由于外生变量，非平稳性，持续性和不稳定性所带来的困难，关于非参数预测回归模型的渐进理论所知甚少。为了克服这些困难，本项目提供上述预测回归模型的理论基础并将所提出的建模方法推广到非平稳和非线性领域。理论上，该项目探索一些新的非参数建模方法以便处理持续的，非平稳的时间序列数据，并提供所得估计的渐进理论结果。可以期望，这些结果将不同于标准非参数模型中的结果。实践中，非参数预测模型的应用将提供更精确更有效的预测结果。

本项目提出三类预测回归模型：半参数预测模型，时变系数预测模型，及可加预测模型。本项目提供上述预测回归模型的理论基础并将所提出的建模方法推广到非平稳和非线性领域。理论上，该项目探索一些新的非参数建模方法以便处理持续的，非平稳的时间序列数据，并提供所得估计的渐进理论结果。这些结果不同于标准非参数模型中的结果并提供更精确更有效的预测。该课题在这方面取得的深入研究成果有以下四方面：.（i）对平稳和非平稳情形, 提出了统一加权估计。.（ii) 建立了相应的渐近理论结果，也建立了关于资产价值可预测性的统一的经验似然比检验。. (iii) 将所提出的方法应用到金融市场数据分析中，并作出了新的发现。. (iv) 对非参数回归模型建立了最近邻估计的极大极小性；对Cox回归模型建立了两阶段抽样情形下有信息缺失时的有效估计。