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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.…

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…

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…

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…

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…

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…

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.

长记忆参数的高阶核半参数 M 估计AI 解读

Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We…

We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency–domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non–normal and has a slow rate of…

分数阶系统中的协整秩确定AI 解读

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a neighbourhood of frequency zero. We first discuss the definition of fractional cointegration. The initial step of cointegration analysis entails partitioning the vector series into subsets with…

谱密度估计与学生化样本均值的 Edgeworth 展开AI 解读

We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the sample mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our…

非平稳时间序列的 Whittle 伪极大似然估计AI 解读

Whittle pseudo-maximum likelihood estimates of parameters for stationary time series have been found to be consistent and asymptotically normal in the presence of long-range dependence. Generalizing the definition of the memory parameter d we extend these results to include possibly nonstationary (.5 ≤ d < 1) or antipersistent (-.5 < d < 0) observations. Using adequate data tapers, we can apply this estimation technique to any degree of nonstationarity d ≥ .5 without a…

市场非均衡模型中的序列相关检验与其他设定分析AI 解读

The assumption of serial independence of disturbances is the starting point of most of the work done on analyzing market disequilibrium models. We derive tests for serial dependence given normality and homoscedasticity using the Lagrange multiplier (LM) test principle. Although the likelihood function under serial dependence is very complicated and involves multiple integrals of dimensions equal to the sample size, the test statistic we obtain through the LM principle is…

含受限因变量模型估计量的渐近性质AI 解读

For the Tobit model with independent observations, Amemiya [1] has established the strong consistency and asymptotic normality of a stationary point, 9, of the log-likelihood. The likelihood for dependent observations may be computationally intractable, so the behavior of 9 in the presence of serially correlated observations is of interest. Under a relaxation of Amemiya's assumption of independence, we prove that 9 is strongly consistent and asymptotically normal, and give…