Time series quantile regression kink with an unknown threshold

This article studies a time series quantile regression kink model with an unknown threshold over certain quantile levels in the distribution. We propose to estimate the threshold parameter and regression parameters using a two-stage method. We also propose a weighted CUSUM test for threshold effect at both a given quantile level and multiple quantile levels based on the subgradient of the quantile loss function. In addition, we consider a likelihood-ratio-type test for the presence of a common threshold value across different quantile levels. Excellent finite sample performance of the proposed method is demonstrated by simulation studies. We further apply our proposed method to the S & P500 index data to explore the possible nonlinearity and heteroscedasticity of the return autocorrelations in the S & P500 index.

本文针对分布中特定分位数水平下带有未知阈值的时间序列分位数回归拐点模型展开研究。我们提出采用两阶段方法对阈值参数与回归参数进行估计。基于分位数损失函数的次梯度，我们针对给定分位数水平与多个分位数水平下的阈值效应，提出了加权累积和（Cumulative Sum, CUSUM）检验。此外，我们还构建了用于检验不同分位数水平下是否存在公共阈值的似然比型检验。模拟研究证实，所提方法具备优异的有限样本表现。最后，我们将所提方法应用于标普500（S&P500）指数数据，以探究标普500指数收益自相关性的潜在非线性与异方差性。