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Extracting a common stochastic trend: Theory with some applications

共同随机趋势的提取:理论与应用

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models--those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that…

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Estimating the structural credit risk model when equity prices are contaminated by trading noises

交易噪声污染股价时的结构信用风险模型估计

The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan [Duan, J.-C., 1994. Maximum likelihood estimation using price data of the derivative contract. Mathematical Finance 4, 155-167] is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via…

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A two-stage realized volatility approach to estimation of diffusion processes with discrete data

基于两阶段已实现波动率的离散观测扩散过程估计

This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002.…

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Quantile cointegrating regression

分位数协整回归

Quantile regression has important applications in risk management, portfolio optimization, and asset pricing. The current paper studies estimation, inference and financial applications of quantile regression with cointegrated time series. In addition, a new cointegration model with quantile-varying coefficients is proposed. In the proposed model, the value of cointegrating coefficients may be affected by the shocks and thus may vary over the innovation quantile. The proposed…

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Forecasts of US short-term interest rates: A flexible forecast combination approach

美国短期利率预测:灵活的预测组合方法

This paper develops a flexible approach to combine forecasts of future spot rates with forecasts from time-series models or macroeconomic variables. We find empirical evidence that, accounting for both regimes in interest rate dynamics, and combining forecasts from different models, helps improve the out-of-sample forecasting performance for US short-term rates. Imposing restrictions from the expectations hypothesis on the forecasting model are found to help at long…

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Assessing value at risk with CARE, the Conditional Autoregressive Expectile models

使用条件自回归期望分位数模型评估风险价值

In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index [theta] of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with distinct tail probabilities under different distributions. Thus, an EVaR…

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A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects

标普500日收益与已实现变差的离散时间模型:跳跃及杠杆效应

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates…

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On the statistical identification of DSGE models

DSGE 模型的统计识别

Dynamic Stochastic General Equilibrium (DSGE) models are now considered attractive by the profession not only from the theoretical perspective but also from an empirical standpoint. As a consequence of this development, methods for diagnosing the fit of these models are being proposed and implemented. In this article we illustrate how the concept of statistical identification, that was introduced and used by Spanos [Spanos, Aris, 1990. The simultaneous-equations model…

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Two estimators of the long-run variance: Beyond short memory

两种长期方差估计量:超越短记忆

This paper deals with the estimation of the long-run variance of a stationary sequence. We extend the usual Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator to deal with long memory and antipersistence. We then derive asymptotic expansions for this estimator and the memory and autocorrelation consistent (MAC) estimator introduced by Robinson [Robinson, P. M., 2005. Robust covariance matrix estimation: HAC estimates with long…

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Central limit theorems and uniform laws of large numbers for arrays of random fields

随机场阵列的中心极限定理与一致大数定律

Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum…

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Fixed effects estimation of structural parameters and marginal effects in panel probit models

面板 Probit 模型中结构参数与边际效应的固定效应估计

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the…

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Reliable inference for the Gini index

基尼系数的可靠推断

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference…

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Edgeworth expansions and normalizing transforms for inequality measures

不平等测度的 Edgeworth 展开与正态化变换

Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and…

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Identification of peer effects through social networks

通过社会网络识别同伴效应

We provide new results regarding the identification of peer effects. We consider an extended version of the linear-in-means model where interactions are structured through a social network. We assume that correlated unobservables are either absent, or treated as network fixed effects. We provide easy-to-check necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although…

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Dynamics of state price densities

状态价格密度的动态变化

State price densities (SPDs) are an important element in applied quantitative finance. In a Black-Scholes world they are lognormal distributions, but in practice volatility changes and the distribution deviates from log-normality. In order to study the degree of this deviation, we estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call pricing function. The estimator is constrained so as to satisfy…

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Tests of risk premia in linear factor models

线性因子模型中风险溢价的检验

We show that statistical inference on the risk premia in linear factor models that is based on the Fama-MacBeth (FM) and generalized least squares (GLS) two-pass risk premia estimators is misleading when the [beta]'s are small and/or the number of assets is large. We propose novel statistics, that are based on the maximum likelihood estimator of Gibbons [Gibbons, M., 1982. Multivariate tests of financial models: A new approach. Journal of Financial Economics 10, 3-27], which…

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Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality

用局部工具变量估计潜在结果分布:大学入学与工资不平等应用

This paper extends the method of local instrumental variables developed by Heckman and Vytlacil [Heckman, J., Vytlacil E., 2005. Structural equations, treatment, effects and econometric policy evaluation. Econometrica 73(3), 669-738] to the estimation of not only means, but also distributions of potential outcomes. The newly developed method is illustrated by applying it to changes in college enrollment and wage inequality using data from the National Longitudinal Survey of…

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Delay times of sequential procedures for multiple time series regression models

多元时间序列回归模型序贯程序的检测延迟

We consider a multiple regression model in which the explanatory variables are specified by time series. To sequentially test for the stability of the regression parameters in time, we introduce a detector which is based on the first excess time of a CUSUM-type statistic over a suitably constructed threshold function. The aim of this paper is to study the delay time associated with this detector. As our main result, we derive the limit distribution of the delay time and…

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Bayesian analysis of random coefficient logit models using aggregate data

使用聚合数据的随机系数Logit模型贝叶斯分析

We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry et al. [Berry, Steven, Levinsohn, James, Pakes, Ariel, 1995. Automobile prices in market equilibrium. Econometrica. 63 (4), 841-890], which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of…

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Semiparametric binary regression models under shape constraints with an application to Indian schooling data

形状约束下的半参数二元回归及印度入学数据应用

We consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable [Delta] is influenced by a set of covariates that can be partitioned as (X,Z) where Z (real valued) is the covariate of primary interest and X (vector valued) denotes a set of control variables. For any fixed X, the conditional…

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Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors

序列相关误差下协整回归有效估计量的渐近性质

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen's [Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99-125] fully modified OLS estimator, Park's [Park, J.Y., 1992. Canonical cointegrating regressions. Econometrica 60, 119-143] canonical cointegrating regression estimator, and Saikkonen's [Saikkonen,…

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Parameter estimation and bias correction for diffusion processes

扩散过程的参数估计与偏差修正

This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous studies, we first develop expansions for the bias and variance of parameter estimators for two of the most employed interest rate processes, Vasicek and CIR processes. Then, we…

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Panel cointegration with global stochastic trends

含全球随机趋势的面板协整

This paper studies estimation of panel cointegration models with cross-sectional dependence generated by unobserved global stochastic trends. The standard least squares estimator is, in general, inconsistent owing to the spuriousness induced by the unobservable I(1) trends. We propose two iterative procedures that jointly estimate the slope parameters and the stochastic trends. The resulting estimators are referred to respectively as CupBC (continuously-updated and…

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