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过滤非平稳成分后的半参数动态 Copula 模型改进估计AI 解读

This paper considers estimation of short-run dynamics in time series that contain a nonstationary component. We assume that appropriate preliminary methods can be applied to the observed time series to separate short-run elements from long-run slowly evolving secular components, and focus on estimation of the short-run dynamics based on the filtered data. We use a flexible copula-generated Markov model to capture the nonlinear temporal dependence in the short-run component…

使用非线性筛方法推断时间序列非参数条件矩限制AI 解读

This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series…

滤除非平稳性的 Copula 时间序列模型AI 解读

Economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We introduce a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We propose two estimators of the copula dependence parameters: the parametric (two-step) copula estimator where…

依赖情形下自归一化的 Cramér 型中等偏差AI 解读

We establish a Cramér-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider three types of self-normalization: the equal-block scheme, the big-block-small-block scheme and the interlacing scheme.…

弱依赖数据下高维矩约束的广义经验似然AI 解读

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment…

可能误设的半非参数时间序列模型的筛推断AI 解读

This paper establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference sequence, the asymptotic variance in the case of irregular functionals is the same as those for independent data. Using an orthonormal series long run variance estimator, we construct a “pre-asymptotic” Wald statistic and show that it is…

非线性与时间依赖AI 解读

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models. We study this link using three measures of temporal dependence: [rho]-mixing, [beta]-mixing and [alpha]-mixing. Stationary diffusions that are [rho]-mixing have mixing coefficients that decay exponentially to zero. When they fail to be [rho]-mixing, they are still [beta]-mixing and [alpha]-mixing; but coefficient decay is slower than exponential. For such processes we…

基于 Copula 的半参数马尔可夫模型的有效估计AI 解读

This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications.…

非线性主成分与多元扩散过程的长期含义AI 解读

We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these NPCs. By exploiting the theory of continuous-time, reversible Markov…

基于 Copula 的非线性分位数自回归AI 解读

Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without…

基于 Copula 的半参数时间序列模型估计AI 解读

This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition distributions are all semiparametric, and a member in this class can be expressed as a generalized semiparametric regression transformation model. One advantage of this copula…

多类 GARCH 与随机波动率模型的混合性和矩性质AI 解读

This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity, existence of higher order moments, geometric ergodicity, and β-mixing with exponential decay rates, which are important properties for statistical inference. As applications, we then provide easy-to-verify sufficient conditions to ensure β-mixing and finite higher order moments…

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…

弱依赖数据下的筛极值估计AI 解读

Many non/semiparametric time series estimates may be regarded as different forms of sieve extremum estimates. For stationary absolute regular mixing observations, the authors obtain convergence rates of sieve extremurn estimates and root-n asymptotic normality of 'plug-in' sieve extremum estimates of smooth functionals. As applications to time series models, they give convergence rates for nonparametric ARX(p,q) regression via neural networks, splines, wavelets; root-n…