Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models
加性单指标协整时间序列模型的稳健 M 估计AI 解读 ↓
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加性单指标协整时间序列模型的稳健 M 估计
- 研究问题
- 面对绝对偏差、分位数及 Huber 等可能非光滑损失，如何分析协整时间序列模型的稳健估计量并建立渐近理论？
- 方法与思路
- 作者利用广义函数及平滑逼近处理非光滑损失，先在简单模型中说明分析范式，再用于加性单指标协整模型的稳健 M 估计。
- 材料陈述的贡献
- 摘要称建立逼近非光滑损失的正则序列收敛速率与估计量渐近理论，并通过模拟和股票收益预测回归展示有限样本表现。
- 阅读关注点
- 应核对广义函数逼近误差与估计误差的衔接、协整及单指标识别条件，以及不同损失函数下的渐近分布和收益预测评价方式。
- 阅读边界
- 所据为 arXiv 预印本，同行评审与期刊接收未核实；摘要未提供具体速率、正则条件或收益预测结果，不能断言全面抗异常值。
原文摘要
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized functions incorporate local integrable functions, the so-called regular generalized functions, while the so-called singular generalized functions (e.g. Dirac delta function) can be obtained as the limits of a sequence of sufficient smooth functions, so-called regular sequence in generalized function context. This makes it possible to use these singular generalized functions through approximation. Nevertheless, a significant contribution of this paper is to establish the convergence rate of regular sequence to nonsmooth loss that answers a call from the relevant literature. For parameter estimation where objective function may be nonsmooth, this paper first shows as a general paradigm that how generalized function approach can be used to tackle the nonsmooth loss functions in Section two using a very simple model. This approach is of general interest and applicability. We further use the approach in robust M-estimation for additive single-index cointegrating time series models; the asymptotic theory is established for the proposed estimators. We evaluate the finite-sample performance of the proposed estimation method and theory by both simulated data and an empirical analysis of predictive regression of stock returns.