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非线性模型时变参数的局部多项式估计AI 解读

We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time-series models, including discrete-valued ones. We show that the proposed estimators are asymptotically normally distributed under weak conditions. We also provide a precise characterization of the leading bias term due to smoothing. We demonstrate the usefulness of our general results by establishing primitive conditions for local…

利用平滑与筛方法求解动态离散选择模型AI 解读

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce smoothed versions of the random…

扩散Copula：识别与估计AI 解读

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations…

Summary We establish nonparametric identification in a class of so-called index models by using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterising the model than those required by existing strategies; in particular, it does not require any large-support conditions on the regressors of our model. We apply the general identification result to additive random…

《计量经济学年鉴》金融与经济间接估计方法专刊导言AI 解读

Introduction \nThis special issue is the outcome of the small and high-powered conference on Indirect Estimation Methods in Finance and Economics. The conference took place at Abbey Hegne in Allensbach (Lake Constance, Germany) on May 2014. It commemorated the 20th anniversary of the seminal papers on Indirect inference of Gourieroux et al. (1993), Simulated quasi-maximum likelihood of Smith Jr. (1993) and the Efficient methods of moments of Gallant and Tauchen (1996).

近似估计量的高阶性质AI 解读

Many modern estimation methods in econometrics approximate an objective function, for instance, through simulation or discretization. These approximations typically affect both bias and variance of the resulting estimator. We first provide a higher-order expansion of such “approximate” estimators that takes into account the errors due to the use of approximations. We show how a Newton–Raphson adjustment can reduce the impact of approximations. Then we use our expansions to…

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…

变换模型的非参数识别与估计AI 解读

This paper derives sufficient conditions for nonparametric transformation models to be identified and develops estimators of the identified components. Our nonparametric identification result is global, and allows for endogenous regressors. In particular, we show that a completeness assumption combined with conditional independence with respect to one of the regressors suffices for the model to be nonparametrically identified. The identification result is also constructive…

含平稳与非平稳协变量的 GARCH-X 模型：拟极大似然估计的渐近理论AI 解读

This article investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE’s) of the GARCH model augmented by including an additional explanatory variable—the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as captured by its long-memory parameter dx; in particular, we allow for both stationary and nonstationary covariates. We show that the QMLE’s of the parameters entering the volatility…

利用显示偏好不等式界定分位数需求函数AI 解读

This paper develops a new approach to the estimation of consumer demand models with unobserved heterogeneity subject to revealed preference inequality restrictions. Particular attention is given to nonseparable heterogeneity. The inequality restrictions are used to identify bounds on counterfactual demand. A nonparametric estimator for these bounds is developed and asymptotic properties are derived. An empirical application using data from the UK Family Expenditure Survey…

非线性协整向量误差修正模型中的检验与推断AI 解读

We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires…

Using nonparametric techniques, we develop a methodology for estimating and testing conditional alphas and betas and long-run alphas and betas, which are the averages of conditional alphas and betas, respectively, across time. The estimators and tests can be implemented for a single asset or jointly across portfolios. The traditional Gibbons, Ross, and Shanken (1989) test arises as a special case of no time variation in the alphas and factor loadings and homoskedasticity. As…

用非参数模拟最大似然估计动态模型AI 解读

We propose an easy-to-implement simulated maximum likelihood estimator for dynamic models where no closed-form representation of the likelihood function is available. Our method can handle any simulable model without latent dynamics. Using simulated observations, we nonparametrically estimate the unknown density by kernel methods, and then construct a likelihood function that can be maximized. We prove that this nonparametric simulated maximum likelihood (NPSML) estimator is…

扩散模型的半非参数估计与设定错误检验AI 解读

Novel transition-based misspecification tests of semiparametric and fully parametric univariate diffusion models based on the estimators developed in [Kristensen, D., 2010. Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models. Journal of Econometrics 156, 239-259] are proposed. It is demonstrated that transition-based tests in general lack power in detecting certain departures from the null since they integrate out local features of the…

非线性误差修正协整模型的似然推断AI 解读

We consider a class of nonlinear vector error correction models where the transfer function (or loadings) of the stationary relationships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties of the process in terms of stochastic and deterministic trends as well as stationary components. In particular, the behavior of the cointegrating relations is described in terms of…

两类半参数扩散模型的伪最大似然估计AI 解读

Two classes of semiparametric diffusion models are considered, where either the drift or the diffusion term is parameterized, while the other term is left unspecified. We propose a pseudo-maximum likelihood estimator (PMLE) of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in. It is demonstrated how models and estimators can be used in a two-step specification testing strategy of semiparametric and fully…

已实现瞬时波动率的非参数滤波：核方法AI 解读

A kernel weighted version of the standard realized integrated volatility estimator is proposed. By different choices of the kernel and bandwidth, the measure allows us to focus on specific characteristics of the volatility process. In particular, as the bandwidth vanishes, an estimator of the realized spot volatility is obtained. We denote this the filtered spot volatility. We show consistency and asymptotic normality of the kernel smoothed realized volatility and the…

异质依赖数据下核估计量的一致收敛速度AI 解读

The main uniform convergence results of Hansen (2008, Econometric Theory 24, 726–748) are generalized in two directions: Data are allowed to (a) be heterogeneously dependent and (b) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving time-inhomogeneous models and/or sampling of continuous-time processes. The usefulness of these results is demonstrated by two applications: kernel regression estimation of a…

偏微分方程估计及其金融应用AI 解读

Linear parabolic partial differential equations (PDE's) and diffusion models are closely linked through the celebrated Feynman-Kac representation of solutions to PDE's. In asset pricing theory, this leads to the representation of derivative prices as solutions to PDE's. Very often implied derivative prices are calculated given preliminary estimates of the diffusion model for the underlying variable. We demonstrate that the implied derivative prices are consistent and derive…

形状不变恩格尔曲线的半非参数工具变量估计AI 解读

This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded…

GARCH(1,1) 模型的闭式估计量AI 解读

We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T(κ−1)/κ-consistency for some κ ∈ (1,2) when the fourth moment exists and…

一类 ARCH(q) 模型准极大似然估计的渐近性质AI 解读

Strong consistency and asymptotic normality are established for the quasi-maximum likelihood estimator for a class of ARCH(q) models. The conditions are that the ARCH process is geometrically ergodic with a moment of arbitrarily small order. Furthermore for consistency, we assume that the second-order moment exists for the nondegenerate rescaled errors and, similarly, that the fourth-order moment exists for asymptotic normality to hold. Contrary to existing literature on…

Consistent standard errors for target variance approach to GARCH estimation.

Consistent standard errors for target variance approach to GARCH estimation.