摘要

Structural instability has been one of the central research questions in economics and finance over many decades. This paper systematically investigates structural instabilities in high dimensional factor models, which portray both structural breaks and threshold effects simultaneously. The observed high dimensional time series are concatenated at an unknown number of break points, while they are described by multiple threshold factor models that are heterogeneous between any two consecutive subsamples. Both joint and sequential procedures for estimating the break points are developed based on the second moment of the pseudo factor estimates that fully ignore the structural instabilities. In each separated subsample, the group Lasso approach recently proposed by Ma and Tu (2023b) is adopted to efficiently identify the threshold factor structure. An information criterion is further proposed to determine the number of break points, which also serves the purpose to distinguish the two types of instabilities. Theoretical properties of the proposed estimators are established, and their finite sample performance is evaluated in Monte Carlo simulations. An empirical application to the U.S. financial market dataset demonstrates the consequences when structural break meets threshold effect in factor analysis.

摘要

Functional coefficient (FC) cointegrating regressions offer empirical investigators flexibility in modeling economic relationships by introducing covariates that influence the direction and intensity of comovement among nonstationary time series. FC regression models are also useful when formal cointegration is absent, in the sense that the equation errors may themselves be nonstationary, but where the nonstationary series display well-defined FC linkages that can be meaningfully interpreted as correlation measures involving the covariates. The present paper proposes new nonparametric estimators for such FC regression models where the nonstationary series display linkages that enable consistent estimation of the correlation measures between them. Specifically, we develop n-consistent estimators for the functional coefficient and establish their asymptotic distributions, which involve mixed normal limits that facilitate inference. Two novel features that appear in the limit theory are (i) the need for non-diagonal matrix normalization due to the presence of stationary and nonstationary components in the regression; and (ii) random bias elements that appear in the asymptotic distribution of the kernel estimators, again resulting from the nonstationary regression components. Numerical studies reveal that the proposed estimators achieve significant efficiency improvements compared to the estimators suggested in earlier work by Sun et al. (2011). Easily implementable specification tests with standard chi-square asymptotics are suggested to check for constancy of the functional coefficient. These tests are shown to have faster divergence rate under local alternatives and enjoy superior performance in simulations than tests proposed in Gan et al. (2014). An empirical application based on the quantity theory of money is included, illustrating the practical use of correlated but non-cointegrated regression relations.

函数系数协整回归通过引入影响非平稳时间序列联动方向与强度的协变量，为经济关系建模提供了灵活的分析框架。即便在形式化协整关系缺失的情况下——即方程误差本身可能非平稳，但只要非平稳序列间存在可明确解释为协变量相关测度的函数系数关联，此类模型仍具实用价值。本文针对这类函数系数回归模型提出了新的非参数估计方法，其适用条件是：非平稳序列间的关联性能保证相关测度的一致性估计。具体而言，我们构建了具有n个一致性的函数系数估计量，并确立了其渐近分布——该分布呈现混合正态极限，便于统计推断。极限理论中显现出两个新颖特征：(i)由于回归中包含平稳与非平稳成分，需采用非对角矩阵标准化；(ii)核估计量的渐近分布中出现随机偏差项，这同样源于回归成分的非平稳性。数值研究表明，相较于Sun等(2011)提出的估计量，新方法能实现显著的效率提升。我们进一步提出易于实施的设定检验（具有标准卡方渐近性）以检测函数系数的恒定性。与Gan等(2014)的检验方法相比，新检验在局部备择下具有更快的发散速率，并在模拟中展现出更优性能。最后，基于货币数量理论的实证应用，生动展示了具有相关性但非协整的回归关系的实际价值。

Quantile prediction with factor-augmented regressiwf测：结构不稳定性与模型不确定性

摘要

分位数回归是建模具有异质性条件分布数据的有效工具。本文研究基于因子增强预测变量的时变系数分位数预测回归模型，旨在同时捕捉平滑的结构性变化并整合高维数据信息进行预测。即使在模型设定存在误判的情况下，我们仍建立了局部线性分位数系数估计量的一致性理论。为进一步提升预测精度，本文创新性地提出基于局部前向验证的时变模型平均方法，证明该平均估计量在最小化样本外预测风险函数意义下具有渐近最优性。此外，我们确立了权重选择的相合性以及平均系数估计量的渐近分布特性。通过数值模拟和预测美国通胀的实际数据应用，验证了所提平均估计方法的优良性能。