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协变量缺失回归模型的识别与推断AI 解读

This paper examines the problem of identification and inference on a conditional moment condition model with missing data, with special focus on the case when the conditioning covariates are missing. We impose no assumption on the distribution of the missing data and we confront the missing data problem by using a worst case scenario approach. We characterize the sharp identified set and argue that this set is usually too complex to compute or to use for inference. Given…

非线性面板固定效应估计的 Bootstrap 与 k 步 Bootstrap 偏差修正AI 解读

Because of the incidental parameters problem, the fixed effects maximum likelihood estimator in a nonlinear panel data model is in general inconsistent when the time series length T is short and fixed. Even if T approaches infinity but at a rate not faster than the cross sectional sample size n , the fixed effects estimator is still asymptotically biased. This paper proposes using the standard bootstrap and k -step bootstrap to correct the bias. We establish the asymptotic…

灵活的非参数条件独立检验AI 解读

This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n −1/2 local power. The test statistic is based on an estimator of the topological “distance” between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the…

未观测异质性的 Neyman C(α) 检验AI 解读

A unified framework is proposed for tests of unobserved heterogeneity in parametric statistic models based on Neyman’s C( α ) approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with respect to the heterogeneity parameter is identically zero, and consequently the conventional Fisher information about the parameter is zero. Nevertheless, local asymptotic optimality of the C( α ) tests can be established via LeCam’s…

计量应用中向随机积分的弱收敛AI 解读

Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on functional weak convergence. In establishing such convergence, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications involve a cointegration framework where endogeneity and nonlinearity play major roles and complicate the limit theory. This paper explores weak convergence…

长自回归何时能够吸收被忽略的参数变化？AI 解读

To construct forecasts for time series exhibiting breaks, the paper examines long autoregressions, where the number of lags is growing with T , and possible breaks are simply ignored. The paper shows that the OLS estimators are still elementwise consistent for the true autoregressive coefficients when neglecting a break in mean, but the sum of the estimators converges to unity. Thanks to this unit-root like behavior of the fitted model, the resulting conditional forecasts…

多重结构变化回归模型的收缩估计AI 解读

In this paper, we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso. We show that with probability tending to one, our method can correctly determine the unknown number of breaks, and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break…

协整多项式回归的完全修正 OLS 估计与推断AI 解读

This paper develops a fully modified OLS (FM-OLS) estimator for cointegrating polynomial regressions, i.e., regressions that include as explanatory variables deterministic variables, integrated processes, and integer powers of integrated processes. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The paper extends the fully modified estimator of Phillips and Hansen (1990) from cointegrating regressions to…

含生成协变量的半参数估计AI 解读

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem…

通过正则化拉普拉斯反演估计波动率占用时间AI 解读

We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in…

正态分布的新刻画与正态性检验AI 解读

We study the asymptotic covariance function of the sample mean and quantile, and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles, if and only if the underlying distribution is normal. This is a powerful result and facilitates statistical inference. Utilizing this result, we develop a new omnibus test for normality based on the quantile-mean covariance…

初始值对非平稳分数时间序列条件平方和估计的影响AI 解读

In this paper, we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter, d , in a nonstationary fractional time series model. The CSS estimator is popular in empirical work due, at least in part, to its simplicity and its feasibility, even in very complicated nonstationary models. We consider a process, X t , for which data…

固定效应自回归模型中的似然推断AI 解读

We calculate the bias of the profile score for the regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted…

条件密度投影的存在性与刻画AI 解读

In this paper we propose primitive conditions under which a projection of a conditional density onto a set defined by conditional moment restrictions exists and is unique. Moreover, we provide an analytic expression of the obtained projection. The range of applications where conditional density projections are used is wide. The derived results are potentially useful in a variety of areas including: semiparametric efficient estimation and optimal testing in (conditional)…

结构门槛回归AI 解读

This paper introduces the structural threshold regression (STR) model that allows for an endogenous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000, Econometrica 68, 575–603) and Caner and Hansen (2004, Econometric Theory 20,…

不同条件变量下条件矩限制模型的半参数效率界AI 解读

This paper addresses the problem of semiparametric efficiency bounds for conditional moment restriction models with different conditioning variables. We characterize such an efficiency bound, that in general is not explicit, as a limit of explicit efficiency bounds for a decreasing sequence of unconditional (marginal) moment restriction models. An iterative procedure for approximating the efficient score when this is not explicit is provided. Our theoretical results provide…

通过非参数滤波估计随机波动率模型AI 解读

A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle…

多元自回归系统与混频数据：一般参数可识别性和估计AI 解读

This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second…

半参数 GARCH 模型的样条估计AI 解读

The semiparametric GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) model of Yang (2006, Journal of Econometrics 130, 365–384) has combined the flexibility of a nonparametric link function with the dependence on infinitely many past observations of the classic GARCH model. We propose a cubic spline procedure to estimate the unknown quantities in the semiparametric GARCH model that is intuitively appealing due to its simplicity. The theoretical properties of…

含单整时间序列的半参数光滑系数模型的一致非参数检验AI 解读

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and…

非平稳非参数回归中核加权样本协方差的一致收敛AI 解读

We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform asymptotic rates depending on direction, a result that differs fundamentally from the random design and stationary cases. The uniform asymptotic rates derived exceed the corresponding rates…

GARCH 模型中平滑结构变化的检测AI 解读

Detecting and modeling structural changes in GARCH processes have attracted increasing attention in time series econometrics. In this paper, we propose a new approach to testing structural changes in GARCH models. The idea is to compare the log likelihood of a time-varying parameter GARCH model with that of a constant parameter GARCH model, where the time-varying GARCH parameters are estimated by a local quasi-maximum likelihood estimator (QMLE) and the constant GARCH…

非同步、微观结构噪声与跳跃并存时的积分协方差估计AI 解读

We propose a new estimator for the integrated covariance of two Itô semimartingales observed at a high frequency. This new estimator, which we call the pre-averaged truncated Hayashi–Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in the case that the sampling schemes of two processes are nonsynchronous and the observation data are polluted by some noise. We also show the asymptotic mixed normality of this estimator…

非参数工具变量回归中泛函的自适应估计AI 解读

We consider the problem of estimating the value ℓ ( ϕ ) of a linear functional, where the structural function ϕ models a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based on a dimension reduction technique and additional thresholding. It is shown that this estimator is consistent and can attain the minimax optimal rate of convergence under additional regularity conditions. This, however, requires an optimal choice…