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具有共同爆炸根的 VAR 回归的不一致性AI 解读

Nielsen (Working paper, University of Oxford, 2009) shows that vector autoregression is inconsistent when there are common explosive roots with geometric multiplicity greater than unity. This paper discusses that result, provides a coexplosive system extension and an illustrative example that helps to explain the finding, gives a consistent instrumental variable procedure, and reports some simulations. Some exact limit distribution theory is derived and a useful new reverse…

一阶差分极大似然与动态面板估计AI 解读

First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that…

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…

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…

幂核异方差与自相关稳健检验的检验力最大化和尺寸控制AI 解读

Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the t -test for different choices of power parameter ( ρ ). We show that the nonstandard fixed- ρ limit distributions of the t -statistic provide more accurate approximations to the finite sample distributions than the conventional large- ρ limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the…

多元与一元扩散过程估计中的偏差AI 解读

Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic…

零能量泛函的渐近理论及非参数回归应用AI 解读

A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In…

衔接局部与适度偏离单位根的极限理论AI 解读

A limit theory is established for autoregressive time series that smooths the transition between local and moderate deviations from unity and provides a transitional form that links conventional unit root distributions and the standard normal. Edgeworth expansions of the limit theory are given. These expansions show that the limit theory that holds for values of the autoregressive coefficient that are closer to stationarity than local (i.e. deviations of the form , where n…

I(1) 数据的自助法AI 解读

A functional law is given for an I(1) sample data version of the continuous-path block bootstrap of Paparoditis and Politis (2001a). The results provide an alternative demonstration that continuous-path block bootstrap unit root tests are consistent under the null.

动态面板模型的间接推断AI 解读

Maximum likelihood (ML) estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size and large cross section sample size asymptotics. This paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference, shows unbiasedness and analyzes efficiency. Monte Carlo studies show that our procedure achieves substantial bias reductions with only mild…

误差密度可能无穷时条件异方差下的 LAD 渐近理论AI 解读

Least absolute deviations (LAD) estimation of linear time series models is considered under conditional heteroskedasticity and serial correlation. The limit theory of the LAD estimator is obtained without assuming the finite density condition for the errors that is required in standard LAD asymptotics. The results are particularly useful in application of LAD estimation to financial time series data.

无限过去初始化下的单位根与协整极限理论AI 解读

It is well known that unit root limit distributions are sensitive to initial conditions in the distant past. If the distant past initialization is extended to the infinite past, the initial condition dominates the limit theory, producing a faster rate of convergence, a limiting Cauchy distribution for the least squares coefficient, and a limit normal distribution for the t -ratio. This amounts to the tail of the unit root process wagging the dog of the unit root limit…

局部极限理论与非参数伪回归AI 解读

A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnostics are suggested for forensic analysis of such regresssions, including a local R…

长记忆与长期变异AI 解读

A commonly used defining property of long memory time series is the power law decay of the autocovariance function. Some alternative methods of deriving this property are considered, working from the alternate definition in terms of a fractional pole in the spectrum at the origin. The methods considered involve the use of (i) Fourier transforms of generalized functions, (ii) asymptotic expansions of Fourier integrals with singularities, (iii) direct evaluation using…

含恒等式结构模型估计的精确分布理论AI 解读

Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV, and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulas for a structural equation model without an identity are shown to apply also to models with an identity by specializing along a certain asymptotic parameter sequence. Some of the new…

基于两阶段已实现波动率的离散观测扩散过程估计AI 解读

This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002.…

局部时密度估计与非参数协整回归的渐近理论AI 解读

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain…

含中度整合与中度爆炸回归变量的协整系统极限理论AI 解读

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form ρ ni = 1 + c i / n α , involving moderate deviations from unity when α ∈ (0, 1) and c i ∈ ℝ are constant parameters. When the data are moderately integrated in the stationary direction (with c i < 0), it is shown that least squares regression is consistent and…

长记忆过程自协方差函数的完整渐近级数AI 解读

An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d[set membership, variant](-1/2,1/2). The class of spectral densities considered includes as a special case the stationary and invertible ARFIMA(p,d,q) model. The leading term of the expansion is of the order O(1/k1-2d), where k is the autocovariance order, consistent with the well known power law decay for such processes, and is…

利用鞅收敛方法研究回归渐近理论AI 解读

Weak convergence of partial sums and multilinear forms in independent random variables and linear processes and their nonlinear analogues to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and conceptually simple method for obtaining such forms of convergence. The method relies on the fact that the econometric quantities of interest involve discrete…

爆炸性协整系统的极限理论AI 解读

A limit theory is developed for multivariate regression in an explosive cointegrated system. The asymptotic behavior of the least squares estimator of the cointegrating coefficients is found to depend upon the precise relationship between the explosive regressors. When the eigenvalues of the autoregressive matrix Θ are distinct, the centered least squares estimator has an exponential Θ n rate of convergence and a mixed normal limit distribution. No central limit theory is…