分位数自回归模型理论与应用研究

发布时间：2018-11-20 12:21

【摘要】：自从1978年Koenker和Bassett提出分位数回归方法以来,在计量经济学的研究领域中涌现了大量的分位数回归模型,分位数自回归(QAR)模型便是其中之一。QAR模型能较好地刻画经济金融序列数据中的非正态性、非对称性和动态性等特征。它是运用分位数回归方法研究时间序列模型的理论起点。近年来,QAR模型越来越受到国外学者的青睐,并已成为时间序列分析领域的研究热点之一。 QAR模型的基本思想是在AR模型框架下,引入分位数回归方法以刻画时间序列中的非对称变化特征。QAR模型提出的时间不长,还有许多问题亟待解决和完善。本文针对QAR模型理论中存在的不足,扩展和改进了现有的QAR模型估计和诊断检验方法,使之能更好地应用于实际经济问题研究。本文的主要创新点如下： (1)在基本QAR模型的基础上,采用蒙特卡罗模拟方法分析了QAR过程的平稳性和样本矩的统计特性,推导了QAR过程的自相关函数,并系统阐述了QAR模型的建模策略。 (2)由于不同分位数回归曲线之间容易出现交叉,这会影响QAR模型估计的准确性。为此,本文对QAR模型的估计方法进行了研究,阐述了三种估计QAR模型回归参数的方法——QR法、RCQR1法和RCQR2法,讨论了这三种估计量的一致性和有限样本性质。研究结论表明,当样本容量较小时,QR法是最理想的估计方法；而在样本容量较大时,RCQR2法的估计效果更好。当QAR模型的误差项服从非正态分布时,RCQR2法在参数估计上的优势尤其明显。 (3)本文模拟分析了有限样本条件下,拟似然比(QLR)统计量在检验QAR模型回归系数显著性的检验尺度和检验功效。结果表明,这种检验方法具有较好的检验功效。基于上述研究,本文提出了序贯检验方法,用于确定QAR模型的最大滞后阶数；比较分析了多种不同滞后阶数选择方法在有限样本条件下的准确性与稳健性。模拟结果显示,基于QLR统计量的序贯检验,尤其是基于supAn统计量的序贯检验,具有较好的有限样本性质,其检验功效显著优于SIC和AIC准则。 (4)在实证研究方面,本文运用QAR模型研究了我国通货膨胀率的持久性及其非对称性动态特征。研究结果表明,不同分位数上的QAR模型的回归系数存在显著差异。从通货膨胀率条件分布的低分位数到高分位数,我国通货膨胀率的持久性不断增强。基于不同分位数τ上的单位根检验结果表明,我国通货膨胀率序列具有总体平稳性和局部非平稳性特征。在受到负向冲击或减速通胀状态下,通货膨胀率序列的变动往往呈现平稳自回归过程：而在受到正向冲击或加速通胀状态下,通货膨胀率序列的变动通常表现为单位根过程。根据QAR模型预测得到的临界分位数值,可以有效区分通货膨胀率变动路径中的平稳点和非平稳点。
[Abstract]:Since Koenker and Bassett put forward the quantile regression method in 1978, a large number of quantile regression models have emerged in the field of econometrics. The quantile autoregressive (QAR) model is one of them, and QAR model can well describe the characteristics of non-normality, asymmetry and dynamics in economic and financial sequence data. It is the theoretical starting point of using quantile regression to study time series model. In recent years, QAR model has been more and more popular among foreign scholars, and has become one of the research hotspots in the field of time series analysis. The basic idea of QAR model is to introduce the quantile regression method to describe the asymmetric variation characteristics in time series under the frame of AR model. The time of QAR model is not long and many problems need to be solved and perfected. Aiming at the deficiency of QAR model theory, this paper extends and improves the existing methods of QAR model estimation and diagnosis, so that it can be better applied to the study of practical economic problems. The main innovations of this paper are as follows: (1) based on the basic QAR model, the stationary and statistical characteristics of the QAR process are analyzed by Monte Carlo simulation, and the autocorrelation function of the QAR process is derived. The modeling strategy of QAR model is expounded systematically. (2) because of the cross between different quantile regression curves, this will affect the accuracy of QAR model estimation. In this paper, the estimation methods of QAR model are studied in this paper. Three methods of estimating regression parameters of QAR model, QR method, RCQR1 method and RCQR2 method, are described. The consistency of the three estimators and the properties of finite samples are discussed. The results show that when the sample size is small, the QR method is the most ideal estimation method, but when the sample size is large, the estimation effect of RCQR2 method is better. When the error term of QAR model is obtained from non-normal distribution, the advantage of RCQR2 method in parameter estimation is particularly obvious. (3) under the condition of finite samples, the quasi-likelihood ratio (QLR) statistics are simulated and analyzed to test the significance of regression coefficient of QAR model. The results show that this method has better test effect. Based on the above research, a sequential test method is proposed to determine the maximum delay order of QAR model, and the accuracy and robustness of many different hysteresis order selection methods under the condition of finite samples are compared and analyzed. The simulation results show that the sequential test based on QLR statistics, especially the sequential test based on supAn statistics, has better properties of finite samples, and its test efficacy is significantly better than that of SIC and AIC criteria. (4) in empirical research, we use QAR model to study the persistence and asymmetric dynamic characteristics of inflation rate in China. The results show that there are significant differences in the regression coefficients of QAR models with different quantiles. From the low quartile to the high quartile of conditional distribution of inflation rate, the persistence of inflation rate in China is increasing. The results of unit root test based on different quantiles 蟿 show that the inflation rate series in China has the characteristics of global stationarity and local nonstationarity. Under the condition of negative shock or deceleration of inflation, the change of inflation rate series tends to be a steady autoregressive process, while under the condition of positive shock or accelerated inflation, the change of inflation rate series is usually expressed as unit root process. According to the critical quantile predicted by QAR model, the stationary point and the non-stationary point in the path of inflation rate change can be effectively distinguished.
【学位授予单位】：南开大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F224;F822.5

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