非线性区间模型及其在经济和金融中的应用

Nonlinear phenomena are general problems in economics and finance, e.g., structural breakpoints, smooth structural changes. However, the existing research only focus on linear interval model. The proposed research firstly attempts to model the nonlinear dynamics of interval-valued data, which captures the nonlinear features of an interval-valued process in economics and finance, and directly produces interval forecasts in practice. One advantage is that more powerful inference and more accurate forecast may be obtained with informational gain of interval-valued data, since it contains the trend or level information (e.g., the two boundaries) and volatility information. This research is mainly divided into four parts, more details as follows. Firstly, a novel sub-system methodology of one-dimensional nonlinear interval modelling will be proposed, including functional coefficient interval models, semiparametric and nonparametric general interval models, and various parametric and nonparametric estimation and corresponding asymptotic theories. Secondly, in terms of two or various nonstationary interval-valued time series, linear and nonlinear co-integration definition, hypothesis and vector error correction interval model(VECIM), including smooth transition VECIM and so on, will be built. Thirdly, linear and nonlinear interval-valued panel models and space models and corresponding asymptotic theories for estimation will be produced. Finally, all these proposed interval models and theories will be applied in economics and finance, e.g., to forecasting the important interval-valued variables, including the GDP growth rate, urban-rural income, stock market indices, foreign exchange rates and so on. And we provide effective approaches of risk management and decision support for the goverment. ..Generally, this research will obtain significant achievements on basic theories and applications, and promote a development of the novel methodology in econometrics proposed by the mainland famous scholars.

非线性特征是经济和金融数据中普遍存在的现象，如渐进式结构变化等。以往的区间计量研究主要局限于线性模型。本项目将建立一套全新的非线性计量理论体系，主要基于区间数据的非线性特征，对非平稳区间样本直接建模，对区间总体进行统计推断。相对于线性模型，非线性区间模型能更好地解释经济和金融中的复杂现象，提高统计推断效率和预测精度。研究包括：(1)建立非线性区间时间序列模型子体系，包括函数型系数区间模型等多种形式，建立多种非参数及参数估计方法和渐近理论；(2)针对多个非平稳区间序列，提出线性及非线性协整区间模型和向量误差修正区间模型子体系；(3)建立线性及非线性区间面板和空间面板模型子体系；(4)应用非线性区间模型分析并预测GDP增速和外汇市场等变量的价格趋势，波动及其拐点，为相关机构提供有效的风险预警方法。本项目的研究将取得一批重要理论和应用成果，推动由中国大陆学者开辟的全新计量经济学方向的发展。

随着信息技术的不断发展，数据更多呈现出复杂数据的特征，其中区间数据为主要代表之一，传统计量和统计分析对这类数据分析不再有效。理论方面，本项目搭建了一系列原创性的非线性区间计量理论体系，包括非线性区间时间序列、线性及非线性区间向量、固定效应区间面板模型，给出了相应模型下的参数估计方法及其统计推断。具体包括阈值区间自回归模型的构建及参数估计的渐近理论、判别阈值效应的假设检验、时变系数区间模型及参数估计的渐近理论、函数型系数的区间模型及其参数估计渐近理论、基于区间向量的脉冲响应、固定效应区间面板模型等。这些新提出的理论工作为经济分析和金融市场的应用研究提供了新的理论视角和方法支撑。应用方面，项目组提出多种区间预测模型，区间事件分析法和区间因子定价模型等，为宏观经济区间管理、金融科技创新和风险管理等方面提供了新方法。区间计量经济学具有非常重要的现实意义，基于区间数据内更多的信息，有助于更新对经济运行态势或金融市场风险的判断，为政府决策部门和相关行业提供有效的分析方法和决策支持。