关于机理变化型变结构非线性协整的研究

变结构非线性协整是协整理论发展的必然的趋势,也是经济系统复杂多变的必然需求,文章补充了变结构非线性协整的定义,并提出了机理变化型变结构非线性协整,指出其本质问题即单位根的结构突变检验,总结了几种结构突变的单位根检验方法,讨论了变结构点的估计方法,给出了基于Chow统计量的变结构协整检验和建模方法。     

时变秩和时变系数VECM模型与“费雪效应”机制检验

研究目标:检验我国经济是否存在“费雪效应”。研究方法:将马尔科夫区制转换结构应用于对协整秩的建模,同时考虑协整参数的时变,构建时变秩和时变系数VECM模型,使用贝叶斯框架估计模型参数。研究发现：1992年1月～2016年3月间我国名义利率与通货膨胀率之间存在时变系数VECM模型与I(1)数据时变系数VAR模型两种区制的转换,我国名义利率和通货膨胀率之间主要表现为时变协整关系。估计的归一化协整向量表明,整个样本期间我国存在“费雪效应”占优;经济“新常态”时期,不存在“费雪效应”处于主导地位;2015年7月以来我国存在时变弱的“费雪效应”。研究创新：将马尔科夫区制转换结构应用于对协整秩的建模,构建时变秩和时变系数VECM模型。研究价值：有助于重新认识“费雪效应之谜”。     

协整向量、调节参数同为非线性的阈值协整检验

针对经济变量的长期均衡和短期调节关系可能同时存在非线性的事实,本文扩展现有阈值协整模型,提出了协整向量、调节参数都为非线性的阈值协整模型,并着重探讨了该模型的检验方法。研究表明,在协整关系的检验中,Wald统计量有较好的有限样本性质。在协整关系的非线性检验中,LMW和LMG统计量的水平扭曲和检验势都较好。在调节参数的非线性检验中,当调节参数具有显著的非线性时,LMH统计量表现出较好的有限样本性质。     

基于门限协整系统的预测方法研究

某些非平稳时间序列，它们在整个区间上并不存在线性协整关系，而存在非线性协整关系。作者运用门限协整的概念，处理非线性协整问题，把整个区间检验为若干个子区间，分别在每个区间上进行线性协整分析。文中讨论了滚动预测方法。最后，通过上证和深证A股指数的门限协整分析，验证了门限协整系统在预测中的优越性。     

面板数据非线性阈值协整的检验方法

非线性阈值协整是线性协整的后续发展。本文使用两机制TR模型对Westerlund和Edgerton(2005)的面板数据协整向量结构突变模型进行扩展,提出截距项具有阈值效应、截距项和斜率系数都具有阈值效应的面板数据非线性阈值协整模型。在此基础上,本文进而分别构造Zc、Ztc、Zr、Ztr统计量检验阈值协整,并对上述统计量的极限分布进行了数学推导,发现它们都收敛于随机泛函。仿真实验结果表明,有限样本下上述检验统计量具有较小的水平扭曲和较高的检验势。     

向量分整序列非线性变换的研究

自Granger提出整数阶单整向量序列的协整概念以来,协整理论在国内外学者的共同努力下不断得到完善。关于向量时间序列的分数维单整的研究主要集中在分整的线性协整的存在性条件及性质研究。文中通过引入交换条件数学期望算法(ACE),研究分整时间序列的非线性变换的协整性,对最优非线性变换函数进行估计。     

非线性误差校正模型中的阈值协整检验——基于阈值协整向量未知的扩展

Kapetanios等(2006)假定阈值协整向量已知,在误差校正模型中使用指数函数刻画非线性调节效应,并使用F懈统计量检验非线性阈值协整.本文基于Kapetanios等(2006)的模型设定,将阈值协整向量由已知扩展为未知,并借鉴Hansen和Seo(2002)的方法估计阈值协整向量和构造F*NEC统计量检验非线性阈值协整.仿真试验表明:本文方法估计的阈值协整向量具有近似无偏、对称的分布和相对较高的精度,并且其随样本容量的变化特征符合一致性.进一步,在有限样本下,F*NEC 与FNEC的水平扭曲没有显著差异,但F*NEC的检验势高于FNEC.     

STAR误差修正模型中协整关系检验的inf-t统计量

在将误差修正过程设定为全局平稳的指数平滑转换函数的情形下,本文建立了一个新的检验统计量 对非线性STAR误差修正模型中的协整关系进行检验;推导了 统计量的渐近分布,并通过Monte Carlo模拟的方式给出了其渐近临界值。 统计量取未识别参数空间上的下确界,有效避免了原假设下的未识别参数问题。Monte Carlo 数值模拟研究的结果表明, 统计量相对E-G两步法的 和Kapetanios等（2006）的 统计量具有更高的检验势。将 统计量应用于对我国货币需求稳定性进行检验,发现我国狭义货币需求量长期稳定,短期存在指数平滑非线性机制转换特征。     

基于参数空间的ST-ECM模型的协整检验问题研究

在非线性平滑转移误差修正模型（ST-ECM）的协整检验中,由于存在未识别参数而使协整检验统计量构造困难,同时由于目前文献普遍使用的泰勒展开近似法并不能精确替代原始非线性模型,从而导致协整检验统计量功效较低。本文首先在遍历未识别参数的参数空间的基础上构造了ST-ECM模型协整检验的supF统计量,推导了supF统计量的极限分布并说明了其收敛性质。接着,蒙特卡洛仿真模拟结果显示,supF统计量在ST-ECM模型协整检验中具有良好的检验水平和功效,且supF统计量的功效明显优于EG统计量、F*NEC统计量和inft统计量。最后,本文对亚洲六个国家的利率期限结构预期假说进行了验证,结果表明中国、新加坡和泰国三个国家的利率期限结构预期假说成立且存在非线性调整效应,supF统计量较其他统计量具有更高的检验功效。     

我国经济周期中菲利普斯曲线机制转移的阈值协整研究

本文应用非线性阈值协整对我国菲利普斯曲线及其在经济周期不同阶段的机制转移进行研究,结果表明我国菲利普斯曲线具有显著的非线性特征,并且非线性转换是由逻辑函数刻画的,转换的位置发生在产出缺口的滞后8个季度。这一结论说明:当产出缺口大于-0.113时,其随后两年的菲利普斯曲线为正斜率;当产出缺口小于-0.113时,其随后两年的菲利普斯曲线为负斜率。菲利普斯曲线随着产出缺口的变化而光滑转换的非线性特征使得我国货币政策的操作效果依赖于已有的经济状态而具有非对称性,进一步,未来两年我国货币政策的操作效果将致使经济增长率与物价指数同向变动。     

Functional-coefficient cointegration models

This paper studies estimation and inference of functional coefficient cointegration models. The proposed model offers a more flexible structure of cointegration where the value of cointegrating coefficients may be affected by informative covariates and thus may vary over time. The model may be viewed as a stochastic cointegration model and includes the conventional cointegration model as a special case. The proposed new model provides a useful complement to the conventional fixed coefficient cointegration models. Both kernel and local polynomial estimators are investigated. Inference procedures for instability of cointegrating parameters and a test for cointegration are proposed based on the functional-coefficient estimates. Limiting distributions of the estimates and testing statistics are derived.     

Quantile cointegrating regression

Quantile regression has important applications in risk management, portfolio optimization, and asset pricing. The current paper studies estimation, inference and financial applications of quantile regression with cointegrated time series. In addition, a new cointegration model with quantile-varying coefficients is proposed. In the proposed model, the value of cointegrating coefficients may be affected by the shocks and thus may vary over the innovation quantile. The proposed model may be viewed as a stochastic cointegration model which includes the conventional cointegration model as a special case. It also provides a useful complement to cointegration models with (G)ARCH effects. Asymptotic properties of the proposed model and limiting distribution of the cointegrating regression quantiles are derived. In the presence of endogenous regressors, fully-modified quantile regression estimators and augmented quantile cointegrating regression are proposed to remove the second order bias and nuisance parameters. Regression Wald tests are constructed based on the fully modified quantile regression estimators. An empirical application to stock index data highlights the potential of the proposed method.     

Stochastic cointegration: estimation and inference

This paper considers the estimation of a stochastically cointegrating regression within the stochastic cointegration modelling framework introduced in McCabe et al. (Stochastic cointegration: testing, 2001). A stochastic cointegrating regression allows some or all of the variables to be conventionally or heteroscedastically integrated. This generalizes Hansen's (J. Econom. 54 (1992) 139) heteroscedastic cointegrating regression model, where the dependent variable is heteroscedastically integrated, but all the regressor variables are restricted to being conventionally integrated. In contrast to conventional and heteroscedastic cointegrating regression, ordinary least-squares (OLS) estimation is shown to be inconsistent, in general, in a stochastically cointegrating regression. As a solution, a new instrumental variables (IVs) estimator is proposed and is shown to be consistent. Under a suitable exogeneity assumption, standard asymptotic inference on the stochastic cointegrating vector can be carried out based on the IV estimator. The finite sample properties of the test statistics, including their robustness to the exogeneity assumption, are examined by simulation.     

Institutional hypothesis of the long-run income velocity of money and parameter stability of the equilibrium relationship

It has recently been argued that when the conventional specification of M2 income velocity is extended to include proxies for two types of institutional change, as emphasized by Bordo and Jonung (1987, 1990), corresponding to the processes of monetization and increasing financial sophistication of financial developments, this extended model is stable in the sense that one can reject the null hypothesis of no cointegration against the alternative of a single cointegrating vector. There may be implications that such an equilibrium relation is a structural income velocity of money function. The evidence based on century-long data from 1880 to 1986 presented in this paper about parameter instability of the cointegrating vector of velocity with its determinants for Canada, Norway, Sweden, and the United Kingdom casts doubt on this interpretation. The evidence is based on using formal stability tests. Moreover, it has an ‘eyeball’ support from the sequential estimates of various parameters of the cointegrating relationship including income and interest semi-elasticities.     

Identifying, estimating and testing restricted cointegrated systems: An overview

The notion of cointegration has led to a renewed interest in the identification and estimation of structural relations among economic time series. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over-identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so-called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.     

Bootstrapping cointegrating regressions

In this paper, we consider bootstrapping cointegrating regressions. It is shown that the method of bootstrap, if properly implemented, generally yields consistent estimators and test statistics for cointegrating regressions. For the cointegrating regression models driven by general linear processes, we employ the sieve bootstrap based on the approximated finite-order vector autoregressions for the regression errors and the first differences of the regressors. In particular, we establish the bootstrap consistency for OLS method. The bootstrap method can thus be used to correct for the finite sample bias of the OLS estimator and to approximate the asymptotic critical values of the OLS-based test statistics in general cointegrating regressions. The bootstrap OLS procedure, however, is not efficient. For the efficient estimation and hypothesis testing, we consider the procedure proposed by Saikkonen [1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21] and Stock and Watson [1993. A simple estimator of cointegrating vectors in higher order integrating systems. Econometrica 61, 783–820] relying on the regression augmented with the leads and lags of differenced regressors. The bootstrap versions of their procedures are shown to be consistent, and can be used to do asymptotically valid inferences. A Monte Carlo study is conducted to investigate the finite sample performances of the proposed bootstrap methods.     

Bayesian Model Selection with an Uninformative Prior*

Bayesian model selection with posterior probabilities and no subjective prior information is generally not possible because of the Bayes factors being ill‐defined. Using careful consideration of the parameter of interest in cointegration analysis and a re‐specification of the triangular model of Phillips (Econometrica, Vol. 59, pp. 283–306, 1991), this paper presents an approach that allows for Bayesian comparison of models of cointegration with ‘ignorance’ priors. Using the concept of Stiefel and Grassman manifolds, diffuse priors are specified on the dimension and direction of the cointegrating space. The approach is illustrated using a simple term structure of the interest rates model.     

Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach

We propose to extend the cointegration rank determination procedure of Robinson and Yajima [2002. Determination of cointegrating rank in fractional systems. Journal of Econometrics 106, 217–242] to accommodate both (asymptotically) stationary and nonstationary fractionally integrated processes as the common stochastic trends and cointegrating errors by applying the exact local Whittle analysis of Shimotsu and Phillips [2005. Exact local Whittle estimation of fractional integration. Annals of Statistics 33, 1890–1933]. The proposed method estimates the cointegrating rank by examining the rank of the spectral density matrix of the d$d$th differenced process around the origin, where the fractional integration order, d$d$, is estimated by the exact local Whittle estimator. Similar to other semiparametric methods, the approach advocated here only requires information about the behavior of the spectral density matrix around the origin, but it relies on a choice of (multiple) bandwidth(s) and threshold parameters. It does not require estimating the cointegrating vector(s) and is easier to implement than regression-based approaches, but it only provides a consistent estimate of the cointegration rank, and formal tests of the cointegration rank or levels of confidence are not available except for the special case of no cointegration. We apply the proposed methodology to the analysis of exchange rate dynamics among a system of seven exchange rates. Contrary to both fractional and integer-based parametric approaches, which indicate at most one cointegrating relation, our results suggest three or possibly four cointegrating relations in the data.