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空间自回归模型的高阶最小二乘推断AI 解读

We develop refined inference for spatial regression models with predetermined regressors. The ordinary least squares estimate of the spatial parameter is neither consistent nor asymptotically normal, unless the elements of the spatial weight matrix uniformly vanish as sample size diverges. We develop refined testing of the hypothesis of no spatial dependence, without requiring such negligibility of spatial weights, by formal Edgeworth expansions. We also develop such…

均值与方差变化的时间序列渐近理论AI 解读

The paper develops point estimation and asymptotic theory with respect to a semiparametric model for time series with moving mean and unconditional heteroscedasticity. These two features are modelled nonparametrically, whereas autocorrelations are described by a short memory stationary parametric time series model. We first study the usual least squares estimate of the coefficient of the first-order autoregressive model based on constant but unknown mean and variance.…

纯空间模型的自适应推断AI 解读

In a general class of semiparametric pure spatial models (having no explanatory variables) allowing nonlinearity in the parameter and the weight matrix, we propose adaptive tests and estimates which are asymptotically efficient in the presence of unknown, nonparametric distributional form. Feasibility of adaptive estimation is verified and its efficiency improvement over Gaussian pseudo maximum likelihood is shown to be either less than, or more than, for models with…

具有长程依赖的曲线时间序列AI 解读

We introduce methods and theory for functional or curve time series with long-range dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed, the conditions for this covering a functional version of fractionally integrated autoregressive moving averages. We also construct an estimate of the long-run covariance function, which we use, via functional principal component analysis, in estimating the orthonormal functions spanning the…

具有个体效应的动态面板数据估计AI 解读

The article discusses statistical inference in parametric models for panel data. The models feature dynamics of a general nature, individual effects, and possible explanatory variables. The focus is on large-cross-section inference on Gaussian pseudo maximum likelihood estimates with temporal dimension kept fixed, partially complementing and extending recent work of the authors. We focus on a particular kind of initial condition but go on to discuss implications of…

具有趋势的面板数据推断AI 解读

Semiparametric panel data modelling and statistical inference with fractional stochastic trends, nonparametrically time-trending individual effects, and general cross-sectional correlation and heteroscedasticity in innovations are developed. The fractional stochastic trends allow for a wide range of nonstationarity, indexed by a memory parameter, nesting the familiar I(1) case and allowing for parametric short-memory. The individual effects can nonparametrically vary…

参数维度增长的空间自回归模型伪极大似然估计AI 解读

Pseudo maximum likelihood estimates are developed for higher-order spatial autoregressive models with increasingly many parameters, including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component, and regression models with spatial autoregressive disturbances. Consistency and asymptotic normality of the estimates are established. Monte Carlo experiments examine finite-sample behaviour.

具有变化均值的非平稳时间序列推断AI 解读

A semiparametric model is proposed in which a parametric filtering of a nonstationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I (1) and other hypotheses are…

横截面相关下的级数估计AI 解读

An asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross-sectional data under conditions on disturbances that allow for forms of cross-sectional dependence and heterogeneity, including conditional and unconditional heteroscedasticity, along with conditions on regressors that allow dependence and do not require existence of a density. The conditions aim to accommodate various settings plausible in economic…

面板空间自相关最大似然推断的高阶修正AI 解读

In a panel data model with fixed effects, possible cross-sectional dependence is investigated in a spatial autoregressive setting. An Edgeworth expansion is developed for the maximum likelihood estimate of the spatial correlation coefficient. The expansion is used to develop more accurate interval estimates for the coefficient, and tests for cross-sectional independence that have better size properties, than corresponding rules of statistical inference based on first order…

空间相关性的精化检验AI 解读

We consider testing the null hypothesis of no spatial correlation against the alternative of pure first order spatial autoregression. A test statistic based on the least squares estimate has good first-order asymptotic properties, but these may not be relevant in small- or moderate-sized samples, especially as (depending on properties of the spatial weight matrix) the usual parametric rate of convergence may not be attained. We thus develop tests with more accurate size…

固定效应面板非参数回归AI 解读

Nonparametric regression is developed for data with both a temporal and a cross-sectional dimension. The model includes additive, unknown, individual-specific components and allows also for cross-sectional and temporal dependence and conditional heteroscedasticity. A simple nonparametric estimate is shown to be dominated by a GLS-type one. Asymptotically optimal bandwidth choices are justified for both estimates. Feasible optimal bandwidths, and feasible optimal regression…

空间相关模型的非嵌套检验AI 解读

We develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all…

参数数量递增的高阶空间自回归模型推断AI 解读

This paper develops consistency and asymptotic normality of parameter estimates for a higher-order spatial autoregressive model whose order, and number of regressors, are allowed to approach infinity slowly with sample size. Both least squares and instrumental variables estimates are examined, and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied. Besides allowing the number of parameters to increase with the data, this…

分数单整固定效应面板模型的有效推断AI 解读

A dynamic panel data model is considered that contains possibly stochastic individual components and a common stochastic time trend that allows for stationary and nonstationary long memory and general parametric short memory. We propose four different ways of coping with the individual effects so as to estimate the parameters. Like models with autoregressive dynamics, ours nests I(1) behaviour, but unlike the nonstandard asymptotics in the autoregressive case, estimates of…

For testing lack of correlation against spatial autoregressive alternatives, Lagrange multiplier tests enjoy their usual computational advantages, but the (χ-super-2) first‐order asymptotic approximation to critical values can be poor in small samples. We develop refined tests for lack of spatial error correlation in regressions, based on Edgeworth expansion. In Monte Carlo simulations, these tests, and bootstrap tests, generally significantly outperform χ-super-2‐based…

误设长期记忆模型的估计AI 解读

We consider time series that, possibly after integer differencing or integrating or other detrending, are covariance stationary with spectral density that is regularly varying near zero frequency, and unspecified elsewhere. This semiparametric framework includes series with short, long and negative memory. We consider the consistency of the popular log-periodogram memory estimate that, conventionally but wrongly, assumes the spectral density obeys a pure power law. The…

存在横截面依赖的非参数趋势回归AI 解读

Panel data, whose series length T is large but whose cross-section size N need not be, are assumed to have common time trend, of unknown form. The model includes additive, unknown, individual-specific components and allows for spatial or other cross-sectional dependence and/or heteroscedasticity. A simple smoothed nonparametric trend estimate is shown to be dominated by an estimate which exploits availability of cross-sectional data. Asymptotically optimal bandwidth choices…

空间依赖回归的统计推断AI 解读

Central limit theorems are developed for instrumental variables estimates of linear and semiparametric partly linear regression models for spatial data. General forms of spatial dependence and heterogeneity in explanatory variables and unobservable disturbances are permitted. We discuss estimation of the variance matrix, including estimates that are robust to disturbance heteroscedasticity and/or dependence. A Monte Carlo study of finite-sample performance is included. In an…

分数阶时间序列模型的高斯伪极大似然估计AI 解读

We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible regions. In these circumstances, a proof of consistency (which is a prerequisite for proving asymptotic normality) can be difficult owing to nonuniform convergence of the objective function over a large admissible parameter space. In particular,…

时变连续时间系统的离散采样AI 解读

We consider a multivariate continuous-time process, generated by a system of linear stochastic differential equations, driven by white noise, and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is…

随机波动模型中的分数协整AI 解读

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility models for the latent variables are employed, in view of their direct application to asset pricing models. Assuming that the underlying persistence is higher in the factor than in the…

ARCH 无穷阶模型的伪极大似然估计AI 解读

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH$(\infty)$ processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particular parameterizations are discussed.

半参数平均导数的 Bootstrap 与 Edgeworth 修正AI 解读

In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the error in the normal approximation, so that refined approximations are of interest, especially in sample sizes that are not enormous. We show that a bootstrap distribution achieves a valid Edgeworth correction in the case of density-weighted averaged…