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弯曲奇异流形上 Metropolis 链的方差与协方差AI 解读

We consider estimation of variance and covariance from a point cloud that are draws from a posterior distribution that lie on a curved, singular manifold. The motivating application is Bayesian inference regarding a likelihood subject to overidentified moment equations using MCMC (Markov Chain Monte Carlo). The MCMC draws lie on a singular manifold that typically is curved. Variance and covariance are Euclidean concepts. A curved, singular manifold is not typically a…

利用惩罚与 MCMC 的约束估计AI 解读

We study inference for parameters defined by either classical extremum estimators or Laplace-type estimators subject to general nonlinear constraints on the parameters. We show that running MCMC on the penalized version of the problem offers a computationally attractive alternative to solving the original constrained optimization problem. Bayesian credible intervals are asymptotically valid confidence intervals in a pointwise sense, providing exact asymptotic coverage for…

过度识别矩条件约束下的非参数贝叶斯估计AI 解读

Nonparametric Bayesian estimation subject to overidentified moment equations is a challenge because the support of the posterior is a manifold of lower dimension than the number of model parameters. The manifold therefore has Lebesgue measure zero thus inhibiting the use of the most commonly used Bayesian estimation method: MCMC (Markov Chain Monte Carlo). This study proposes an effective MCMC algorithm and algorithms for estimating scale and the normalizing constant. The…

互补的贝叶斯矩方法策略AI 解读

Summary Methodology is proposed that addresses two problems that arise in application of the generalized method of moments representation of the likelihood in Bayesian inference: (1) a missing Jacobian term and (2) a normality assumption. The proposals are illustrated by application to the seminal application of the generalized method of moments methodology in the econometric literature: an endowment economy whose representative agent has constant relative risk aversion…

Itô半鞅短时变动分布的精确贝叶斯矩推断AI 解读

We modify the Gallant and Tauchen (1996) efficient method of moments (EMM) method to perform exact Bayesian inference, where exact means no reliance on asymptotic approximations. We use this modification to evaluate the empirical plausibility of recent predictions from high frequency financial theory regarding the small-time movements of an Itô semimartingale. The theory indicates that the probability distribution of the small moves should be locally stable around the…

含少量或大量异质参与者及潜在序列相关状态的动态模型：贝叶斯估计AI 解读

We propose a Bayesian approach to estimating dynamic models that can have state variables that are latent, serially correlated, and heterogeneous. Our approach employs sequential importance sampling and is based on deriving an unbiased estimate of the likelihood within a Metropolis chain. Under fairly weak regularity conditions unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. Results are verified by Monte Carlo…

利用矩条件进行状态空间模型的贝叶斯估计AI 解读

We consider Bayesian estimation of state space models when the measurement density is not available but estimating equations for the parameters of the measurement density are available from moment conditions. The most common applications are partial equilibrium models involving moment conditions that depend on dynamic latent variables (e.g., time–varying parameters, stochastic volatility) and dynamic general equilibrium models when moment equations from the first order…

一般科学模型的确定及其资产定价应用AI 解读

We consider a consumption-based asset pricing model that uses habit persistence to overcome the known statistical inadequacies of the classical consumption-based asset pricing model. We find that the habit model fits reasonably well and agrees with results reported in the literature if conditional heteroskedasticity is suppressed but that it does not fit nor do results agree if conditional heteroskedasticity, well known to be present in financial market data, is allowed to…

随机波动率模型期权价格计算的高斯近似方案AI 解读

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from…

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连续时间扩散过程极大似然估计的数值技术AI 解读

Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, since the transition density is generally unknown, one is forced to approximate it. The simulation-based approach suggested by Pedersen (1995) has great theoretical appeal, but…

A common model for security price dynamics is the continuous-time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the Black-Scholes price with the forward integrated variance replacing the Black-Scholes variance. Implementing the Hull and White characterization requires both estimates of the price dynamics and the conditional distribution of the forward integrated variance given…

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应该匹配哪些矩？AI 解读

We describe an intuitive, simple, and systematic approach to generating moment conditions for generalized method of moments (GMM) estimation of the parameters of a structural model. The idea is to use the score of a density that has an analytic expression to define the GMM criterion. The auxiliary model that generates the score should closely approximate the distribution' of the observed data but is not required to nest it. If the auxiliary model nests the structural model…

SNP 密度估计量的收敛速度AI 解读

The SNP density estimator is a truncation (or sieve) estimator based upon a Hermite series expansion. Other nonparametric estimators based on orthogonal series expansions have been proposed.

非线性动态结构AI 解读

Methods for nonlinear impulse response analysis are introduced. The methods are based on conditional moment profiles defined for a stationary time series. Comparing conditional moment profiles to baseline profiles is the nonlinear analog of conventional impulse-response analysis. The bootstrap may be used for statistical inference. Profile bundles may be examined for evidence of damping or persistence. Application to bivariate NYSE price and volume series from 1928 to 1987…

具有光滑随机效应密度的非线性混合效应模型AI 解读

The fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood. The density of the random effects is assumed to be smooth but is otherwise unrestricted. The method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood. Standard algorithms are used for optimization. Empirical Bayes estimates of random coefficients are…

用非参数回归估计混沌系统的李雅普诺夫指数AI 解读

We discuss procedures based on nonparametric regression for estimating the dominant Lyapunov Exponent λ1 from time series data generated by a nonlinear autoregressive system with additive noise. For systems with bounded fluctuations, λ1 > 0 is the defining feature of chaos. Thus our procedures can be used to examine time series data for evidence of chaotic dynamics. We show that a consistent estimator of the partial derivatives of the autoregression function can be used to…

实现渐近正态性的半非参数估计量自适应规则AI 解读

In econometrics, seminonparametric (SNP) estimators originated in the consumer demand literature. The Fourier flexible form is a well-known example. The idea is to replace the consumer's indirect utility function with a truncated series expansion and then use a parametric procedure, such as nonlinear multivariate regression, to set a confidence interval on an elasticity. More recently, SNP estimators have been used in nonlinear time series analysis. A truncated Hermite…

条件约束异质过程的半非参数估计：资产定价应用AI 解读

A. Ronald Gallant, George Tauchen, Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications, Econometrica, Vol. 57, No. 5 (Sep., 1989), pp. 1091-1120

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半非参数最大似然估计AI 解读

Often maximum likelihood is the method of choice for fitting an econometric model to data but cannot be used because the correct specific ation of (multivariate) density that defines the likelihood is unknown. In this situation, simply put the density equal to a Hermite series and apply standard finite dimensional maximum likelihood methods. Model parameters and nearly all aspects of the unknown density itself will be estimated consistently provided that the length of the…