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条件矩限制下的弱识别稳健检验AI 解读

Abstract We propose a semiparametric test for the value of coefficients in models with conditional moment restrictions that has correct size regardless of identification strength. The test is in essence an Anderson-Rubin (AR) test using nonparametrically estimated instruments to which we apply a standard error correction. We show that the test is (1) always size-correct, (2) consistent when identification is not too weak, and (3) asymptotically equivalent to an infeasible AR…

增广 HEGY 季节单位根检验AI 解读

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for…

平稳边界附近的均值与自协方差函数估计AI 解读

We analyze the applicability of standard normal asymptotic theory for linear process models near the boundary of stationarity. Limit results are given for estimation of the mean, autocovariance and autocorrelation functions within the broad region of stationarity that includes near boundary cases which vary with the sample size. The rate of consistency and the validity of the normal asymptotic approximation for the corresponding estimators is determined both by the sample…

非标准条件下的最优估计AI 解读

We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek–Le Cam optimality theory is adapted to cover this situation. We show that the expectation of certain monotone “bowl-shaped” functions of the squared estimation…

时变方差模型中的协整秩选择AI 解读

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient Cn→∞ and Cn/n→0 as n→∞. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and…

分数协整系统的精确局部 Whittle 估计AI 解读

Semiparametric estimation of a bivariate fractionally cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (δ<1/2) and nonstationary (δ≥1/2) stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and…

非平稳时间序列模型中的稳健推断AI 解读

This paper studies robust inference in unit root and cointegration models. The analysis covers a range of important inference problems including testing stationarity against unit roots, testing for structure change in nonstationary regressions, and testing for cointegration. We analyze these inference problems in a unified regression framework, although separate analysis is given for each specific case when it is needed. The proposed inference procedures are constructed…

含超前项与滞后项的协整回归模型选择准则AI 解读

In this paper, Mallows’ (1973)Cp criterion, Akaike’s (1973) AIC, Hurvich and Tsai’s (1989) corrected AIC and the BIC of Akaike (1978) and Schwarz (1978) are derived for the leads-and-lags cointegrating regression. Deriving model selection criteria for the leads-and-lags regression is a nontrivial task since the true model is of infinite dimension. This paper justifies using the conventional formulas of those model selection criteria for the leads-and-lags cointegrating…

过程非平稳时基于平稳性的扩散模型设定检验AI 解读

We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We consider integrated and explosive processes, as well as nearly integrated ones in the spirit of the local to unity analysis in classical unit root theory. We find that the behavior of the test predicted by the asymptotic distribution under an integrated process provides a better…

趋势与初始条件双重不确定性下的单位根检验AI 解读

In this paper we provide a joint treatment of two major problems that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, and uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. We suggest decision rules based on the union of rejections of four standard unit root tests (OLS and quasi-differenced demeaned and detrended ADF unit root tests), along…

带漂移随机游走指数的和AI 解读

For many time series in empirical macro and finance, it is assumed that the logarithm of the series is a unit root process. Since we may want to assume a stable growth rate for the macroeconomics time series, it seems natural to potentially model such a series as a unit root process with drift. This assumption implies that the level of such a time series is the exponential of a unit root process with drift and therefore, it is of substantial interest to investigate…

采用新轮廓的面板单位根检验AI 解读

The paper introduces a novel approach to testing for unit roots in panels, which takes a new contour that is drawn along the line given by the equi-squared-sum instead of the traditional one given by the equi-sample-size. We show in the paper that the distributions of the unit root tests are asymptotically normal along the new contour under both the null and the local-to-unity alternatives. Subsequently, we demonstrate that this startling finding may be exploited…

连续时间模型中均值回复参数估计的偏差AI 解读

It is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in finite discrete samples and in large in-fill samples. In this paper, we obtain two expressions to approximate the bias of the least squares/maximum likelihood estimator of the mean reversion parameter in the Ornstein–Uhlenbeck process with a known long run mean when discretely sampled data are available. The first…

超越面板单位根检验：用多重检验识别各序列的非平稳性AI 解读

Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of n individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we suggest and demonstrate how…

为什么采样频率会影响金融时间序列的单位根检验AI 解读

It is generally believed that the power of unit root tests is determined only by the time span of observations, not by their sampling frequency. We show that the sampling frequency does matter for stock data displaying fat tails and volatility clustering, such as financial time series. Our claim builds on recent work on unit root testing based on non-Gaussian GARCH-based likelihood functions. Such methods yield power gains in the presence of fat tails and volatility…

非参数协整回归中的动态误设AI 解读

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya–Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a “pseudo-true function” limit that is a local average of the true regression function. In this respect…

弱识别下的非线性协整回归AI 解读

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite-sample distributions of nonlinear least squares estimators, resulting in…

白噪声中的单位根AI 解读

We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T )/ p → 0 and p 3 / T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p , we…

自回归模型的统一区间估计AI 解读

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal without assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based…

非线性非平稳模型的设定检验AI 解读

We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain…

相关面板中基于残差的协整检验AI 解读

In the paper, we propose residual based tests for cointegration in general panels with cross-sectional dependency, endogeneity and various heterogeneities. The residuals are obtained from the usual least squares estimation of the postulated cointegrating relationships from each individual unit, and the nonlinear IV panel unit root testing procedure is applied to the panels of the fitted residuals using as instruments the nonlinear transformations of the adaptively fitted…

使用柯西估计量的异方差面板单位根检验AI 解读

The Cauchy estimator of an autoregressive root uses the sign of the first lag as instrumental variable. The resulting IV t-type statistic follows a standard normal limiting distribution under a unit root case even under unconditional heteroscedasticity, if the series to be tested has no deterministic trends. The standard normality of the Cauchy test is exploited to obtain a standard normal panel unit root test under cross-sectional dependence and time-varying volatility with…

非平稳波动下单位根检验的自助法联合检验AI 解读

Three important issues surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data; uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not, and the possible presence of nonstationary volatility in the data. Assuming homoskedasticity, Harvey, Leybourne, and Taylor (2011, Journal of Econometrics , forthcoming) propose decision rules based on a four-way union of…

随机系数面板模型中的单位根检验AI 解读

This paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model, in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance. The asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples.