复合分位数下门限自回归模型的变点估计

Combined change point estimation in threshold quantile autoregressive models

金融领域中的突发事件是变点问题的一种体现,往往由于其随机性和发生前信息量不足等因素造成突发事件难以识别和预测.金融市场常常表现出非线性和异质性等特征,门限分位数自回归模型作为金融领域变点问题研究的重要模型,逐渐在经济和统计学界获得更多的关注.本文结合不同的分位数对门限分位数自回归模型中的变点估计问题提出两种新的估计方法:门限自回归分位数复合估计和分位数平均估计.在一些实际数据分析中,研究发现在不同分位数水平下门限分位数自回归模型中的变点非常接近.基于变点的这种共同性,首先通过最小化不同分位数下的联合损失函数得到更有效的复合变点估计,并进一步推导复合变点估计量的渐近性质,以及基于似然比和自助法构建所提出估计量的置信区间.其次,通过对不同分位数下的变点估计量求平均提出另一种复合分位数估计方法,即门限分位数平均估计,并给出相应的大样本性质.数值模拟研究发现,相比传统的门限最小二乘估计和分位数估计,所提出的两种方法在有限样本条件下更加有效.最后,分析2005–2014年上证A股指数展示所提出方法的实际应用表现.

The financial market is a typical complex system,and we can find its expressions in the complexity of nonlinearity and heterogeneity of the market.In order to mine for more meaningful information,the threshold quantile autoregressive model regarded as an effective method has become very popular in econometrics and statistics.We propose two new methods for estimating the change point,which are the composite quantile regression estimator and the quantile average estimator.By combining quantile regression over multiple quantiles,these proposed methods improve estimation accuracy and efficiency of change points under the assumption of constant thresholds.In some actual data analysis,we find that the change points in the threshold quantile autoregressive model are very close on different quantile levels.Due to the commonality of the change points,we first obtain a more efficient change point estimator by minimizing the combined quantile objective function across different quantiles.We further derive the asymptotic properties and build the confidence interval based on likelihood ratio and bootstrap methods of the composite change point estimator.Second,we propose an alternative estimator that is the quantile average estimator by averaging the quantile-specific slope estimators involved in the estimation procedure at different quantiles.In general,the results of numerical simulation show that the proposed methods have higher estimation efficiency compared with the traditional ordinary least squares estimator and the quantile threshold estimator under limited sample conditions.Finally,we analyze the empirical application performance of the proposed method with the A-share index of Shanghai Stock Exchange from 2005 to 2014.