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Low-frequency robust cointegration testing

低频稳健协整检验

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data’s persistence. This paper considers low-frequency tests about cointegrating vectors under a range of restrictions on the common stochastic trends. We quantify how much power can potentially be gained by exploiting correct restrictions, as well as the magnitude of size distortions if such…

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Model averaging by jackknife criterion in models with dependent data

依赖数据模型中基于刀切准则的模型平均

The past decade witnessed a literature on model averaging by frequentist methods. For the most part, the asymptotic optimality of various existing frequentist model averaging estimators has been established under i.i.d. errors. Recently, Hansen and Racine [Hansen, B.E., Racine, J., 2012. Jackknife model averaging. Journal of Econometrics 167, 38–46] developed a jackknife model averaging (JMA) estimator, which has an important advantage over its competitors in that it…

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Predicting binary outcomes

二元结果预测

We address the issue of using a set of covariates to categorize or predict a binary outcome. This is a common problem in many disciplines including economics. In the context of a prespecified utility (or cost) function we examine the construction of forecasts suggesting an extension of the Manski (1975, 1985) maximum score approach. We provide analytical properties of the method and compare it to more common approaches such as forecasts or classifications based on…

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Panel data models with multiple time-varying individual effects

具有多个时变个体效应的面板数据模型

This paper considers a panel data model with time-varying individual effects. The data are assumed to contain a large number of cross-sectional units repeatedly observed over a fixed number of time periods. The model has a feature of the fixed-effects model in that the effects are assumed to be correlated with the regressors. The unobservable individual effects are assumed to have a factor structure. For consistent estimation of the model, it is important to estimate the…

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Evaluating treatment protocols using data combination

利用数据组合评估处理分配规则

In real life, individuals are often assigned to binary treatments according to existing treatment protocols. Such protocols, when designed with “taste-based” motives, would be productively inefficient in that the expected returns to treatment for a marginal treatment recipient would vary across covariates and be larger for discriminated groups. This cannot be directly tested if assignment is based on more covariates than the researcher observes, because then the marginal…

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On the structure and estimation of hierarchical Archimedean copulas

层级阿基米德 Copula 的结构与估计

In this paper we provide a method for estimating multivariate distributions defined through hierarchical Archimedean copulas. In general, the true structure of the hierarchy is unknown, but we develop a computationally efficient technique to determine it from the data. For this purpose we introduce a hierarchical estimation procedure for the parameters and provide an asymptotic analysis. We consider both parametric and nonparametric estimation of the marginal distributions.…

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Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions

任意初始条件下面板 AR(1) 模型的准最大似然估计

In this paper we show that the Quasi ML estimation method yields consistent Random and Fixed Effects estimators for the autoregression parameter ρ in the panel AR(1) model with arbitrary initial conditions and possibly time-series heteroskedasticity even when the error components are drawn from heterogeneous distributions. We investigate both analytically and by means of Monte Carlo simulations the properties of the QML estimators for ρ. The RE(Q)MLE for ρ is asymptotically…

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Powerful tests for structural changes in volatility

波动率结构变化的高功效检验

Detecting structural changes in volatility is important for understanding volatility dynamics and stylized facts observed for financial returns such as volatility persistence. We propose modified CUSUM and LM tests that are built on a robust estimator of the long-run variance of squared series. We establish conditions under which the new tests have standard null distributions and diverge faster than standard tests under the alternative. The theory allows smooth and abrupt…

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Chi-squared tests for evaluation and comparison of asset pricing models

资产定价模型评估与比较的卡方检验

This paper presents a general statistical framework for estimation, testing and comparison of asset pricing models using the unconstrained distance measure of Hansen and Jagannathan (1997). The limiting results cover both linear and nonlinear models that could be correctly specified or misspecified. We propose modified versions of the existing model selection tests and new pivotal specification and model comparison tests with improved finite-sample properties. In addition,…

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Maximum likelihood estimation and uniform inference with sporadic identification failure

局部识别失效下的最大似然估计与一致推断

This paper analyzes the properties of a class of estimators, tests, and confidence sets (CSs) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter θ. This includes log likelihood, quasi-log likelihood, and least squares criterion functions.

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Semi-parametric estimation of American option prices

美式期权价格的半参数估计

We introduce a novel semi-parametric estimator of American option prices in discrete time. The specification is based on a parameterized stochastic discount factor and is nonparametric w.r.t. the historical dynamics of the Markovian state variables. The historical transition density estimator minimizes a distance built on the Kullback–Leibler divergence from a kernel transition density, subject to the no-arbitrage restrictions for a non-defaultable bond, the underlying asset…

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Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach

检验连续时间过程是否为扩散过程:基于无穷小算子的方法

We develop a nonparametric test to check whether a process can be represented by a stochastic differential equation driven only by a Brownian motion. Our testing procedure utilizes the infinitesimal operator-based martingale characterization combined with a generalized spectral approach. Such a testing procedure is feasible and convenient because the infinitesimal operator of the diffusion process has a closed-form expression. The proposed test is applicable to both…

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On loss functions and ranking forecasting performances of multivariate volatility models

损失函数与多元波动模型预测表现的排序

The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of non-metric distance measures of the Bregman type which…

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One-step R-estimation in linear models with stable errors

稳定分布误差线性模型中的一步秩估计

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators remain root-n consistent (the optimal rate) under the whole family of stable distributions, irrespective…

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Extended Neyman smooth goodness-of-fit tests, applied to competing heavy-tailed distributions

扩展 Neyman 光滑拟合优度检验及重尾分布比较

A simplified version of the Neyman (1937) “Smooth” goodness-of-fit test is extended to account for the presence of estimated model parameters, thereby removing overfitting bias. Using a Lagrange Multiplier approach rather than the Likelihood Ratio statistic proposed by Neyman greatly simplifies the calculations. Polynomials, splines, and the step function of Pearson’s test are compared as alternative perturbations to the theoretical uniform distribution. The extended tests…

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Moment condition tests for heavy tailed time series

重尾时间序列的矩条件检验

We develop an asymptotically chi-squared statistic for testing moment conditions E[mt(θ0)]=0, where mt(θ0) may be weakly dependent, scalar components of mt(θ0) may have an infinite variance, and E[mt(θ)] need not exist for any θ under the alternative. Score tests are a natural application, and in general a variety of tests can be heavy-tail robustified by our method, including white noise, GARCH affects, omitted variables, distribution, functional form, causation, volatility…

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Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration

多元 Ornstein–Uhlenbeck 过程的统计估计及协整应用

Ornstein–Uhlenbeck models are continuous-time processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate Ornstein–Uhlenbeck model driven by a multivariate regularly varying Lévy process with infinite variance. We show that the estimator is consistent. Moreover, we derive its…

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The method of simulated quantiles

模拟分位数法

We introduce the Method of Simulated Quantiles, or MSQ, an indirect inference method based on quantile matching that is useful for situations where the density function does not have a closed form and/or moments do not exist. Functions of theoretical quantiles, which depend on the parameters of the assumed probability law, are matched with the sample counterparts, which depend on the observations. Since the theoretical quantiles may not be available analytically, the…

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Estimation for multivariate stable distributions with generalized empirical likelihood

利用广义经验似然估计多元稳定分布

This paper considers the generalized empirical likelihood (GEL) method for estimating the parameters of the multivariate stable distribution. The GEL method is considered to be an extension of the generalized method of moments (GMM). The multivariate stable distributions are widely applicable as they can accommodate both skewness and heavy tails. We treat the spectral measure, which summarizes scale and asymmetry, by discretization. In order to estimate all the model…

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Model identification for infinite variance autoregressive processes

无穷方差自回归过程的模型识别

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order…

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Heavy tails of OLS

普通最小二乘估计量的重尾性质

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from…

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Stable mixture GARCH models

稳定分布混合 GARCH 模型

A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its…

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