中度偏离单位根过程：理论发展与比较
来源：中国社会科学网
【作者单位】
郭刚正：华中科技大学经济学院。
【摘要】研究目标：中度偏离单位根过程，是指自回归系数偏离于单位根但其偏离成分随着样本长度推移而逐渐回复到单位根的时间序列自回归过程。本文对中度偏离单位根过程的研究进行了归纳总结，并揭示中度偏离单位根相关过程的理论联系与差异。研究方法：本文基于自回归系数与单位根的关系，建立起单位根过程、近单位根过程、近中度偏离单位根过程、中度偏离单位根过程以及爆炸过程的统一框架，并以中度偏离单位根过程为枢纽，从模型设定、数据特征、样本统计量收敛速度和极限分布等层面将上述自回归过程有机地衔接起来。研究发现：中度偏离单位根过程有效地磨平了不同自回归过程下系数估计偏误的收敛速度和极限分布等渐近性质的不连续性。本文所提出的中度偏离单位根t检验具有不依赖于冗杂参数和维纳过程的标准分布。研究创新：以统一的视角剖析不同类别自回归过程的联系与差异，从分布函数的角度出发寻找中度偏离单位根过程向单位根过程和爆炸过程转化的边界点。这在国内外文献上尚属首次。研究价值：中度偏离单位根检验为进一步深刻认识经济时间序列数据的特征和理解市场运行的状态提供了可信的计量工具。
【关键词】中度偏离单位根过程; 单位根过程; 爆炸过程; 渐近理论
【基金项目】本文获得国家自然科学基金面上项目“中度偏离、泡沫与单位根过程的结构变化理论和应用研究——我国供给侧改革和金融监管的理论和实证依据”（71671070）和华中科技大学人文社会科学发展专项基金资助。
Moderate Deviations from a Unit Root：
Theoretical Development and Comparison
ABSTRACT: Research Objectives: The moderate deviation from a unit root is an autoregressive model where the autoregressive root is greater than unity but its deviation from unity decreases as the sample size increases. This paper summarizes the existing research on the moderate deviation process, and reveals the theoretical connection and difference of the related autoregressive processes. Research Methods: Based on the relationship between the autoregressive root and unity, we establish a unified framework for the standard unit root process, the local-to-unity process, the local-to-moderate deviation process, the moderate deviation process, and the explosive process. This framework takes full advantage of the characteristics of the moderate deviation process, and links the above autoregressive processes from the aspects of model setting, data characteristics, convergence speed and limiting distribution. Research Findings: The results show that the moderate deviation process effectively smoothes the discontinuity of the asymptotic properties of coefficient estimation errors under different autoregressive processes. The moderate deviation t-test proposed in the paper has a standard limiting distribution that does not depend on nuisance parameters and Wiener processes. Research Innovations: To our best knowledge, this is the first paper in the literature to establish a general framework for different autoregressive models. Research Value: This study provides a credible econometric tool for understanding the characteristics of economic time series data and the state of market operations.
KEY WORDS: Moderate Deviation from a Unit Root; Unit Root ; Explosive Process; Asymptotic Theory
