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季节性单位根假设的有效检验AI 解读

In this paper we derive, under the assumption of Gaussian errors with known error covariance matrix, asymptotic local power bounds for seasonal unit root tests for both known and unknown deterministic scenarios and for an arbitrary seasonal aspect. We demonstrate that the optimal test of a unit root at a given spectral frequency behaves asymptotically independently of whether unit roots exist at other frequencies or not. We also develop modified versions of the optimal tests…

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存在多次水平突变的自回归单位根检验AI 解读

The asymptotic distributions of augmented Dickey–Fuller (ADF) unit root tests for autoregressive processes with a unit or near-unit root are discussed in the presence of multiple stochastic level shifts of large size occurring independently in time. The distributions depend on a Brownian motion and a Poisson-type jump process. Due to the latter, tests based on standard critical values experience power losses increasing rapidly with the number and the magnitude of the shifts.…

检测单位根与平稳性的序贯监测程序AI 解读

When analyzing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0) or I(1) property. Fixed-sample statistical tests for that problem are well studied in the literature. In this paper we provide first results for the problem of monitoring sequentially a time series. Our stopping times are based on a sequential version of a kernel-weighted…

动态系统中的协整搜索AI 解读

, which can be zero, stable cointegrating vectors against the alternative hypothesis of more than r0 cointegrating vectors existing in some subsample. The tests proposed follow Breitung (2002). They are non-parametric in nature and are invariant to linear transformations of the series. A distinctive feature is that they allow us to detect the hidden cointegration when the system is affected by an unknown number of regime changes of unknown timing. We analyse the limiting…

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平稳分数协整的局部 Whittle 分析及隐含与已实现波动率的关系AI 解读

I consider local Whittle analysis of a stationary fractionally cointegrated model. The local Whittle quasi maximum likelihood estimator is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The proposed estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. I show that the…

长面板协整模型的统计推断AI 解读

This article presents a general likelihood-based framework for inference in panel vector autoregressive (VAR) models with cointegration restrictions. The cointegrating relationships are restricted to each cross section while the rest of the model is unrestricted. The homogeneous restriction of common cointegrating space is also considered. Asymptotic distributions of parameter estimators and the test statistics for the cointegrating rank and the homogeneous restriction are…

基于 VAR 近似的协整检验修正信息准则AI 解读

We consider the cointegration tests of Johansen (1988, Journal of Economic Dynamics and Control 12, 231–254; 1991, Econometrica 59, 1551–1580) when a vector autoregressive (VAR) process of order k is used to approximate a more general linear process with a possibly infinite VAR representation. Traditional methods to select the lag order, such as Akaike's information criterion (AIC) or the Bayesian information criterion, often lead to too parsimonious a model with the…

I(2) 模型协整秩的似然比检验AI 解读

This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25–59), Paruolo (1996, Journal of Econometrics 72, 313–356), and Rahbek, Kongsted, and…

单位根不变检验的可用信息AI 解读

This paper considers the information available to invariant unit root tests at and near the unit root. Because all invariant tests will be functions of the maximal invariant, the Fisher information in this statistic will be the available information. The main finding of the paper is that the available information for all tests invariant to a linear trend is zero at the unit root. This result applies for any sample size, over a variety of distributions and correlation…

单位根附近无约束信息矩阵估计量的不一致性AI 解读

converges to a non-degenerate random variable and contributes to the asymptotic distribution of a Wald test for the null hypothesis of a random walk versus a stable AR(1) alternative. With this newly derived asymptotic distribution, the above Wald test is found to improve its performance. A non-local criterion of asymptotic relative efficiency based on Bahadur slopes has been employed for the first time to the problem of unit root testing. The Wald test derived in the paper…

单位根检验的稳健贝叶斯方法AI 解读

In this paper we deal with the identification of an autoregressive model for an observed time series and the detection of a unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We consider a Bayesian approach, and particular attention is devoted to the problem of the sensitivity of the standard Bayesian analysis with respect to the…

向量自回归过程的单整阶数AI 解读

We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996, Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models) is proved.I am very grateful to Søren Johansen for his precious insights and his…

协方差平稳与单位根面板 AR(1) 模型的有效线性 GMM 估计AI 解读

This paper considers generalized method of moments (GMM) estimation of the inclusive panel AR(1) model that contains the covariance stationary panel AR(1) model and the panel AR(1) model with a unit root as special cases. The paper presents a two-step optimal linear GMM (OLGMM) estimator for the inclusive model that is asymptotically equivalent to the optimal nonlinear GMM estimator of Ahn and Schmidt (1997, Journal of Econometrics 76, 309–321) when the data are covariance…

三变量 VAR 过程长期因果关系的有效检验：货币—收入关系的滚动窗口研究AI 解读

Abstract This paper develops a simple sequential multiple‐horizon non‐causation test strategy for trivariate VAR models (with one auxiliary variable). We apply the test strategy to a rolling window study of money supply and real income, with the price of oil, the unemployment rate and the spread between the Treasury bill and commercial paper rates as auxiliary processes. Ours is the first study to control simultaneously for common stochastic trends, sensitivity of test…

利用非线性协整估计货币需求函数AI 解读

Abstract Conventionally, the money demand function is estimated using a regression of the logarithm of money demand on either the interest rate or the logarithm of the interest rate. This equation is presumed to be a cointegrating regression. In this paper, we aim to combine the logarithmic specification, which models the liquidity trap better than a linear model, with the assumption that the interest rate itself is an integrated process. The proposed technique is robust to…

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针对近积分过程的修正 KPSS 检验AI 解读

This note suggests a simple modification to the Kwiatkowski, Phillips, Schmidt, and Shin (1992, Journal of Econometrics , 54, 159–178) test (KPSS test) so that it is applicable to testing the null hypothesis of near integration against a unit root alternative. The modified KPSS test is shown not to suffer from the asymptotic size distortion problems of the original KPSS test that are described by Müller (2005, Journal of Econometrics 128, 195–213). The test also has good…

单位根检验能否区分单位根过程与平稳非线性过程？AI 解读

Standard unit-root tests are known to be biased towards the non-rejection of a unit-root when they are applied to time series with non-linear dynamics. Unfortunately, not much is known about the source of the power loss mainly because the analysis on nonstationarity and nonlinearity to this date has been fragmentary. By means of a Monte Carlo study, the current paper investigates the finite sample performance of five popular unit-root tests against a wide class of non-linear…

单整结构动态模型的滞后增广两阶段与三阶段最小二乘估计AI 解读

We consider a lag-augmented two- or three-stage least-squares estimator for a structural dynamic model of non-stationary and possibly cointegrated variables without the prior knowledge of unit roots or rank of cointegration. We show that the conventional two-and three-stage least-squares estimators are consistent but contain non-standard distributions without the strict exogeneity assumption; hence the conventional Wald type test statistics may not be chi-square distributed.…