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非平稳分数单整序列的渐近理论AI 解读

In this paper, we study the asymptotics of nonstationary fractional integrated time series, the long memory time series with d ≥ ½, with special attention focused on the cases when d = (2 p + 1)/2 for integer n no less than 0. There is considerable empirical evidence showing long memory of this magnitude in many economic time series including the inflation rate and the stock market volatility. A study of the large-sample property is therefore both needed and useful. Also, we…

伪结构断点现象札记AI 解读

When the disturbances of a regression model follow an I (1) process there is a tendency to estimate a break point in the middle of the sample, even though a break point does not actually exist. In this note, we provide a mathematical proof for this phenomenon.

计算 ARMA 模型自协方差的新方法：精确形式解AI 解读

In this article we present a new method for computing the theoretical autocovariance function of an autoregressive moving average model. The importance of our theorem is that it yields two interesting results: First, a closed-form solution is derived in terms of the roots of the autoregressive polynomial and the parameters of the moving average part. Second, a sufficient condition for the lack of model redundancy is obtained.

基于固定平滑参数核密度估计量的拟合优度检验AI 解读

In this paper, we study the bias-corrected test developed in Fan (1994). It is based on the integrated squared difference between a kernel estimator of the unknown density function of a random vector and a kernel smoothed estimator of the parametric density function to be tested under the null hypothesis. We provide an alternative asymptotic approximation of the finite-sample distribution of this test by fixing the smoothing parameter. In contrast to the normal approximation…

用于非平稳性检验的零频自回归谱密度估计量AI 解读

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant…

非中心二次型统计量的鞍点近似AI 解读

Many estimators and tests are of the form of a ratio of quadratic forms in normal variables. Excepting a few very special cases little is known about the density or distribution of these ratios, particularly if we allow for noncentrality in the quadratic forms. This paper assumes this generality and derives saddlepoint approximations for this class of statistics. We first derive and prove the existence of an exact inversion based on the joint characteristic function. Then…

非识别模型中的信念更新AI 解读

A Bayesian analysis of a nonidentified model is always possible if a proper prior on all the parameters is specified. There is, however, no Bayesian free lunch. The “price” is that there exist quantities about which the data are uninformative, i.e., their marginal prior and posterior distributions are identical. In the case of improper priors the analysis is problematic—resulting posteriors can be improper. This study investigates both proper and improper cases through a…

变量选择后回归中的有效置信区间AI 解读

We consider a linear regression model with regression parameters (θ 1 ,...,θ p ) and error variance parameter σ 2 . Our aim is to find a confidence interval with minimum coverage probability 1 − α for a parameter of interest θ 1 in the presence of nuisance parameters (θ 2 ,...,θ p ,σ 2 ). We consider two confidence intervals, the first of which is the standard confidence interval for θ 1 with coverage probability 1 − α. The second confidence interval for θ 1 is obtained…

样本选择模型的有效半参数评分估计AI 解读

A semiparametric likelihood method is proposed for the estimation of sample selection models. The method is a two-step semiparametric scoring estimation procedure based on an index restriction and kernel estimation. Under some regularity conditions, the estimator is square-root n -consistent and asymptotically normal. The estimator is also asymptotically efficient in the sense that its asymptotic covariance matrix attains the semiparametric efficiency bound under the index…

基于凸核的 M 估计量渐近理论AI 解读

We study the convergence in distribution of M -estimators over a convex kernel. Under convexity, the limit distribution of M -estimators can be obtained under minimal assumptions. We consider the case when the limit is arbitrary, not necessarily normal. If some Taylor expansions hold, the limit distribution is stable. As an application, we examine the limit distribution of M -estimators for the multivariate linear regression model. We obtain the distributional convergence of…

以时间序列为基础的计量经济学AI 解读

Since the influential work by Nelson and Plosser (1982) and Engle and Granger (1987), many new and exciting developments have been made in the analysis of time series involving autoregressive unit roots. Hatanaka (1996; hereafter HT) reviewed the literature on unit roots and cointegration up to 1994 and provided new perspectives on this research area.

趋势函数突变对 Dickey–Fuller 单位根检验的影响AI 解读

This article analyzes the asymptotic behavior of the Dickey–Fuller unit root tests when the variable is generated under the breaking trend hypothesis. Our results show that the asymptotic behavior of these statistics allows for the rejection of the unit root hypothesis. This asymptotic finding contrasts with the results that can be found in the literature devoted to the analysis of the integration order of a variable in the presence of a structural break. However, some Monte…

重尾随机变量的卡方型分布AI 解读

The distribution of sums of squared random variables with heavy-tailed distributions is investigated. Considering random variables in the domain of attraction of a stable Paretian law we derive the limiting distribution as the degrees of freedom approach infinity. The finite-degrees-of-freedom behavior for stable Paretian variates is simulated. Response surface techniques are employed to compactly summarize the simulation results for a relevant range of significance levels.

含 MA 单位根的 ARMA 模型估计AI 解读

This paper investigates the behavior of the maximum likelihood estimator of a Gaussian autoregressive moving average model with a unit root in the moving average polynomial. The results are primarily of interest in testing hypotheses that involve moving average unit roots as, for example, when testing for stationarity of a series.

仅在备择下存在干扰参数的一致设定检验AI 解读

The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bear closely on recent developments in artificial neural networks.…

Hilbert 空间值依赖异质数组的中心极限定理与函数中心极限定理及应用AI 解读

We obtain new central limit theorems (CLT's) and functional central limit theorems (FCLT's) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT's for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent…

扩散过程的准间接推断AI 解读

We discuss an estimation procedure for continuous-time models based on discrete sampled data with a fixed unit of time between two consecutive observations. Because in general the conditional likelihood of the model cannot be derived, an indirect inference procedure following Gouriéroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8, 85–118) is developed. It is based on simulations of a discretized model. We study the asymptotic properties of this…

协整系统中的结构变化检验AI 解读

This paper considers tests for structural change of the cointegrating vector and the adjustment vector in the error correction model with an unknown change point. This paper derives new tests for structural change, which are applicable to maximum likelihood estimation. Our tests for structural change of the cointegrating vector have the same nonstandard asymptotic distributions that have been found by Hansen (1992a, Journal of Business and Economic Statistics 10, 321–335).…

季节单位根的 Phillips–Perron 型检验AI 解读

In this paper we consider a semiparametric version of the test for seasonal unit roots suggested by Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238). The asymptotic theory is based on the analysis of a simple regression problem, and the results apply to tests at any given frequency in the range (0,π]. Monte Carlo simulations suggest that the test may have more power than the parametric test of Hylleberg et al. (1990). On the other hand, the…

单整向量自回归过程的参数化刻画AI 解读

This paper provides a polynomial factorization theorem that is then used to extend the characterization parts of the parametric representation theorems of Johansen (1992, Econometric Theory 8, 188–202) for vector autoregressive processes integrated of up to order 2. A characterization theorem is provided in the general case of an I ( d ) process. For the discussion of the complicated polynomial cointegration properties of such processes, the case of an I (3) process is…

条件对称性的一致设定检验AI 解读

This paper presents a consistent specification test of conditional symmetry using a kernel method. The test statistic is shown to be asymptotically distributed as standard normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distribution. Power against local alternatives is also investigated. A Monte Carlo simulation is provided to evaluate the finite-sample performance of the test.

误差修正模型的自适应估计AI 解读

This paper considers adaptive maximum likelihood estimation of reduced rank vector error correction models. It is shown that such models can be asymptotically efficiently estimated even in the absence of knowledge of the shape of the density function of the innovation sequence, provided that this density is symmetric. The construction of the estimator, involving the nonparametric kernel estimation of the unknown density using the residuals of a consistent preliminary…

条件分位数约束下参数回归模型的一致非参数检验AI 解读

This paper proposes a nonparametric, kernel-based test of parametric quantile regression models. The test statistic has a limiting standard normal distribution if the parametric quantile model is correctly specified and diverges to infinity for any misspecification of the parametric model. Thus the test is consistent against any fixed alternative. The test also has asymptotic power 1 against local alternatives converging to the null at proper rates. A simulation study is…

未知形式异方差下的自相关检验AI 解读

This paper develops a test of autocorrelation in the presence of heteroskedasticity of unknown form in the nonlinear regression model. The test statistic is based on the sample autocovariance of the residuals standardized by a nonparametric kernel estimate of the unknown heteroskedasticity function. Under appropriate conditions, the test statistic is shown to have a limiting chi-square distribution. Local power and consistency results for the test are also established. Monte…