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共同随机趋势检验AI 解读

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is…

矩阵秩的检验AI 解读

This paper considers tests for the rank of a matrix for which a root- T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator's asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables.…

协整与信息集之间的距离AI 解读

This paper investigates Granger noncausality and the cointegrating relation between two time series in the Hilbert space framework. This framework allows us to analyze the relationship between cointegration and distance between two information sets. In particular, we prove that if two variables, X and Y , are cointegrated, then the distance between two information sets, concerning the differenced series Δ X and Δ Y , must be less than the standard deviation of Δ X .

非高斯对数周期图回归AI 解读

We show the consistency of the log-periodogram regression estimate of the long memory parameter for long range dependent linear, not necessarily Gaussian, time series when we make a pooling of periodogram ordinates. Then, we study the asymptotic behavior of the tapered periodogram of long range dependent time series for frequencies near the origin, and we obtain the asymptotic distribution of the log-periodogram estimate for possibly non-Gaussian observation when the tapered…

系数具有马尔可夫切换的向量自回归过程的若干性质AI 解读

Some statistical properties of a vector autoregressive process with Markov-switching coefficients are considered. Sufficient conditions for this nonlinear process to be covariance stationary are given. The second moments of the process are derived under the conditions. The autocovariance matrix decays at exponential rate, permitting the application of the law of large numbers. Under the stationarity conditions, although sharing the “mean-reverting” property with conventional…

正态尺度混合分布下的贝叶斯回归分析AI 解读

This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in…

平稳 ARCH 模型：依赖结构与中心极限定理AI 解读

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

《计量经济学方法》书评AI 解读

The fourth edition of Econometric Methods by Jack Johnston and John DiNardo, is a rewrite of the venerable third edition by Johnston that sustained several generations of economists. As stated by the authors themselves, the reason for undertaking this major revision is to provide a comprehensive and accessible account of currently available econometric methodology, and in my opinion they have been successful in achieving their objective. The book has 13 chapters and runs to…

《基于模拟的计量经济学方法》书评AI 解读

The accessibility of high-performance computing power has always influenced theoretical and applied econometrics. Gouriéroux and Monfort begin their recent offering, Simulation-Based Econometric Methods , with a stylized three-stage classification of the history of statistical econometrics. In the first stage, lasting through the 1960's, models and estimation methods were designed to produce closed-form expressions for the estimators. This spurred thorough investigation of…

《动态非线性计量模型：渐近理论》书评AI 解读

Benedikt Pötscher and Ingmar Prucha are two exceptional econometricians who combine an extraordinary knowledge of the statistics and econometrics literature with great analytical skills. Both are excellent mathematicians, and the comment that can be heard among mathematicians that econometricians are “self-made mathematicians” definitely does not apply to them. Therefore, given the task of writing an overview of asymptotic theory for minimization estimators for dependent…

协整对数似然比检验渐近分布的近似AI 解读

Tail approximation of the asymptotic distribution of the log likelihood ratio test for cointegration in a vector autoregressive process is studied. In dimension 2, an approximation of weighted χ 2 type is derived by applying multivariate saddlepoint approximation techniques to a Fourier inversion integral.

长记忆依赖下 Durbin–Watson 统计量的渐近理论AI 解读

In time series regression models with “short-memory” residual processes, the Durbin–Watson statistic ( DW ) has been used for the problem of testing for independence of the residuals. In this paper we elucidate the asymptotics of DW for “long-memory” residual processes. A standardized Durbin–Watson statistic ( SDW ) is proposed. Then we derive the asymptotic distributions of SDW under both the null and local alternative hypotheses. Based on this result we evaluate the local…

GARCH(p,q) 过程的四阶矩结构AI 解读

In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH( p , q ) process is given and also an expression for the moment itself. Furthermore, the autocorrelation function of the centered and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as the GARCH(2,2) process and the ARCH( q ) process.

具有 AR(1) 扰动的不等间隔面板数据回归AI 解读

This paper deals with the estimation of unequally spaced panel data regression models with AR(1) remainder disturbances. A feasible generalized least squares (GLS) procedure is proposed as a weighted least squares that can handle a wide range of unequally spaced panel data patterns. This procedure is simple to compute and provides natural estimates of the serial correlation and variance components parameters. The paper also provides a locally best invariant test for zero…

利用函数迭代对数律界限区分 I(0) 与 I(1)AI 解读

We construct properly scaled functions of R p -valued partial sums of demeaned data and derive bounds via the functional law of the iterated logarithm for strong mixing processes. If we obtain a value below or equal to the bound we decide in favor of I (0); otherwise we decide in favor of I (1). This provides a consistent rule for classifying time series as being I (1) or I (0). The nice feature of the procedure lies in the almost sure nature of the bound, guaranteeing a lim…

积分条件矩检验的最优性AI 解读

This paper proposes a version of the integrated conditional moment (ICM) test that is optimal for a class of composite alternatives. The ICM test is built on the fact that a random function based on a correctly specified model should have zero mean, whereas any misspecification in the conditional mean implies a divergent mean for the random function. We derive test statistics that are optimal for each basis element of an orthonormal decomposition of the function space for…

若干分数单整检验的局部渐近功效AI 解读

It is possible to construct a test of the null of no fractional integration that has nontrivial asymptotic power against a sequence of alternatives specifying that the series is I ( d ) with d = O ( T −1/2 ), where T is the sample size. In this paper, I show that tests for fractional integration that are based on the partial sum process of the time series have only trivial asymptotic power (i.e., equal to the size) against this sequence of local alternatives. These tests…

具有时变系数的协整回归AI 解读

This paper considers cointegrating regressions with time varying coefficients. The coefficients are modeled as smooth functions evolving over time. It is shown that they can be estimated nonparametrically, using suitably modified series estimators. Presented is the efficient method of estimation, which relies on simple prefiltering of the data and preestimation of the model. The test for the adequacy of model specification is also developed. Our model and statistical methods…

非平稳分数单位根AI 解读

This paper deals with a scalar I ( d ) process { y j }, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with { y j }, assuming that d is known and is greater than or equal to ½. Note that { y j } becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality…

具有无限方差误差的 I(1) 过程之间的伪回归AI 解读

This paper considers spurious regression between integrated processes with stable errors. Our results show that the t -ratios diverge at the rate of √T, which is identical to what Phillips (1986, Journal of Econometrics 33, 311–340) has obtained for the Gaussian case. Therefore, it is the long memory in the dependent variable and regressors, instead of the moment conditions of the error terms, that causes the spurious regression.

具有分数单整误差的协整时间序列渐近推断AI 解读

Vector valued autoregressive models with fractionally integrated errors are considered. The possibility of the coefficient matrix of the model having eigenvalues with absolute values equal or close to unity is included. Quadratic approximation to the log-likelihood ratios in the vicinity of auxiliary estimators of the parameters is obtained and used to make a rough identification of the approximate unit eigenvalues, including complex ones, together with their multiplicities.…

协整回归中的有效去趋势AI 解读

This paper studies efficient detrending in cointegrating regression and develops modified tests for cointegration that use efficient detrending procedures. Asymptotics for these tests are derived. Monte Carlo experiments are conducted to evaluate the detrending procedures in finite samples and to compare tests for cointegration based on different detrending procedures. The limit theory allows for increasingly remote initial condition effects as the sample size goes to…

具有多种隐含单位根的多元时间序列：第二部分AI 解读

This paper extends the statistical results obtained by Gregoir and Laroque (1994, Journal of Econometrics 63, 183–214). It develops statistical tools to analyze multivariate time series that can be represented under an autoregressive equation of finite order with various polynomial error correction terms at various frequencies with possibly a non-null deterministic part as introduced by Gregoir (1999, Econometric Theory 15, 435–468). We propose an estimation procedure that…

具有多种隐含单位根的多元时间序列：第一部分AI 解读

Following the approach proposed by Gregoir and Laroque (1993, Econometric Theory 9, 329–342), we consider a class of multivariate processes that, when differenced enough, yields covariance stationary processes whose determinant of the matrix series associated with their Wold representation has various unit roots with various orders of multiplicity we restrict to be integers. A representation theorem is provided that involves different polynomial error correction terms at…