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“札记与问题”：问题与解答系列的新形式AI 解读

In establishing the Problems and Solutions (P&S) series of Econometric Theory , the primary objective was pedagogical—to provide an intellectual resource for students, instructors, and researchers through the publication of student exercises and research-level problems in econometrics. Over the past 20 years, the P&S series has successfully served this goal. Large numbers of worked exercises and problems have now been published, and the series has promoted interaction…

一种简单的时间序列正态性检验AI 解读

This paper considers testing for normality for correlated data. The proposed test procedure employs the skewness-kurtosis test statistic, but studentized by standard error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities that do not incorporate any downweighting, and, hence, no smoothing parameter is needed. Therefore, the main feature of our proposed test is its…

近积分模型中回归型季节单位根检验统计量的渐近分布AI 解读

In this paper we derive representations for the limiting distributions of the regression-based seasonal unit root test statistics of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) and Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), inter alia, when the underlying process displays near seasonal integration. Our results generalize those presented in previous studies by allowing for an arbitrary seasonal periodicity (including the…

VAR(1) 过程的 I(2) 模型：问题 04.3.1AI 解读

This problem discusses an I (2) model in the VAR(1) case. The I (2) representation theorem of Johansen (1992) (JRT) holds also for VAR(1) processes. The I (2) model for VAR( k ) processes has been discussed for k ≥ 2 in Johansen (1996, Ch. 9; 1997). We here discuss a parametrization for the I (2) case of VAR(1) that differs from the VAR( k ) model.

关于“复单位根与商业周期：它们真实吗？”的札记AI 解读

This note discusses the concept of aliasing and its use in the paper by H.J. Bierens (2001, Econometric Theory 17, 962–983), in the framework of a second-order autoregression with complex unit roots. The condition on the range of the angular frequency φ is extended to φ ∈ (0,2π) − {π}.Financial support from UPV-EHU research project 9/UPV-00038.321-13503/2001, Basque Government project PI9970 and Ministerio de ciencia y tecnología BEC2003-02028 is gratefully acknowledged.

“积分时间序列非线性变换的渐近理论”补遗AI 解读

Typically in time series econometrics, for many statistics, a rescaled integrated process is replaced with Brownian motion to find the limit distribution. For averages of functions of a rescaled integrated process, Park and Phillips have shown that this remains true for functions with poles, as long as a sample-size-dependent region around the poles is excluded from consideration, the function is locally integrable, and some other regularity conditions hold. In this…

同时建模条件异方差与尺度变化AI 解读

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard generalized autoregressive conditional heteroskedastic (GARCH) model so that conditional heteroskedasticity (CH) and scale change in financial returns can be modeled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic properties of the estimators are…

伯恩斯坦 Copula 及其在多元分布建模与逼近中的应用AI 解读

We define the Bernstein copula and study its statistical properties in terms of both distributions and densities. We also develop a theory of approximation for multivariate distributions in terms of Bernstein copulas. Rates of consistency when the Bernstein copula density is estimated empirically are given. In order of magnitude, this estimator has variance equal to the square root of the variance of common nonparametric estimators, e.g., kernel smoothers, but it is biased…

误设独立同分布模型中的有效矩估计法AI 解读

The paper presents the asymptotic theory of the efficient method of moments when the model of interest is not correctly specified. The paper assumes a sequence of independent and identically distributed observations and a global misspecification. It is found that the limiting distribution of the estimator is still asymptotically normal, but it suffers a strong impact in the covariance matrix. A consistent estimator of this covariance matrix is provided. The large sample…

长记忆协变量过程下的回归模型拟合检验AI 解读

This paper proposes some tests for fitting a regression model with a long memory covariate process and with errors that form either a martingale difference sequence or a long memory moving average process, independent of the covariate. The tests are based on a partial sum process of the residuals from the fitted regression. The asymptotic null distribution of this process is discussed in some detail under each set of these assumptions. The proposed tests are shown to have…

分数差分参数极大似然估计量的分布展开AI 解读

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6/π2). This paper develops asymptotic expansions to the distribution of this statistic under the assumption of a known unit variance. The correction term for the density is shown to be independent of d, so that the MLE is second-order pivotal for d. This feature of the MLE is unusual, at least in time series contexts.…

风险率函数的平均导数AI 解读

This paper develops semiparametric kernel-based estimators of risk-specific hazard functions for competing risks data. Both discrete and continuous failure times are considered. The maintained assumption is that the hazard function depends on explanatory variables only through an index. In contrast to existing semiparametric estimators, proportional hazards is not assumed. The new estimators are asymptotically normally distributed. The estimator of index coefficients is…

面板协整：合并时间序列检验的渐近与有限样本性质及购买力平价应用AI 解读

We examine properties of residual-based tests for the null of no cointegration for dynamic panels in which both the short-run dynamics and the long-run slope coefficients are permitted to be heterogeneous across individual members of the panel. The tests also allow for individual heterogeneous fixed effects and trend terms, and we consider both pooled within dimension tests and group mean between dimension tests. We derive limiting distributions for these and show that they…

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04.2.2 Hermitian 投影矩阵的刻画AI 解读

Let P in be a projector with P + its Moore–Penrose inverse and P H its conjugate transpose. Werner (2002) provides a list of equivalent conditions for P to be Hermitian.

04.2.1 含正交投影矩阵的分块矩阵值域等式AI 解读

When considering the general Gauss–Markov model Y = X β + e , where E ( e ) = 0, Cov( e ) = V , one often needs to know whether the range inclusion range( X ) ⊆ range( V ) holds.

新西兰计量经济学研究组庆祝格兰杰获诺奖：第十二届会议报告AI 解读

The 12th meeting of the New Zealand Econometrics Study Group (NZESG) was held in Wellington at the Reserve Bank of New Zealand on Friday afternoon, 17 October 2003, and at Old Government Buildings, Victoria University, on Saturday, 18 October 2003. It was well attended by approximately 50 participants (7 from overseas) with a full program of 20 speakers, including an opening address by Dr Alan Bollard, Governor, Reserve Bank of New Zealand. Full details of the program,…

谱表示定理所用逼近的若干问题AI 解读

In many important textbooks the formal statement of the spectral representation theorem is followed by a process version, usually informal, stating that any stationary stochastic process {ξ(t), t ∈ T} is the limit in quadratic mean of a sequence of processes {S(n,t), t ∈ T}, each consisting of a finite sum of harmonic oscillations with stochastic weights. The natural issues, whether the approximation error ξ(t) − S(n,t) is stationary or whether at least it converges to zero…

时间序列模型的广义 Portmanteau 拟合优度检验AI 解读

We present a goodness-of-fit test for time series models based on the discrete spectral average estimator. Unlike current tests of goodness of fit, the asymptotic distribution of our test statistic allows the null hypothesis to be either a short- or long-range dependence model. Our test is in the frequency domain, is easy to compute, and does not require the calculation of residuals from the fitted model. This is especially advantageous when the fitted model is not a…

部分根接近一时完全修正 VAR 假设检验的稳健性AI 解读

This paper proves that the fully modified vector autoregression (FM-VAR) estimator has second-order bias effects when some roots are local to unity. These bias effects are shown to result in potentially severe size distortions in FM-VAR testing when the hypothesis involves near unit root variables. In addition, the paper reveals that with the FM-VAR method near unit roots become estimated as exact unit roots with convergence speed faster than the order of the sample size.…

协整平滑转换回归AI 解读

This paper studies the smooth transition regression model where regressors are I(1) and errors are I(0). The regressors and errors are assumed to be dependent both serially and contemporaneously. Using the triangular array asymptotics, the nonlinear least squares estimator is shown to be consistent, and its asymptotic distribution is derived. It is found that the asymptotic distribution involves a bias under the regressor-error dependence, which implies that the nonlinear…

半参数广义可加模型中的 Bootstrap 推断AI 解读

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric…

基于经验似然的推断及其在若干计量模型中的应用AI 解读

This paper uses the concept of dual likelihood to develop some higher order asymptotic theory for the empirical likelihood ratio test for parameters defined implicitly by a set of estimating equations. The resulting theory is likelihood based in the sense that it relies on methods developed for ordinary parametric likelihood models to obtain valid Edgeworth expansions for the maximum dual likelihood estimator and for the dual/empirical likelihood ratio statistic. In…

稳健单位根检验不应被“修改”AI 解读

The rank-based unit root tests proposed by Hasan and Koenker (1997, Econometrica 65, 133–161) have power equal to size for normal innovations. Unit root tests based on M-estimators exhibit the same behavior. The problem occurs because the test statistics are transformed to obtain computationally convenient critical values. I describe a convenient way to compute critical values without transforming the test statistics. The resulting tests are almost as powerful as least…