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Extremum estimation and numerical derivatives

极值估计与数值导数

Finite-difference approximations are widely used in empirical work to evaluate derivatives of estimated functions. For instance, many standard optimization routines rely on finite-difference formulas for gradient calculations and estimating standard errors. However, the effect of such approximations on the statistical properties of the resulting estimators has only been studied in a few special cases. This paper investigates the impact of commonly used finite-difference…

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Identification and estimation in a correlated random coefficients binary response model

相关随机系数二元响应模型的识别与估计

We study a linear index binary response model with random coefficients B allowed to be correlated with regressors X. We identify the mean of the distribution of B and show how the mean can be interpreted as a vector of expected relative effects. We use instruments and a control vector V to make X independent of B given V. This leads to a localize-then-average approach to both identification and estimation. We develop a n-consistent and asymptotically normal estimator of a…

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Structural-break models under mis-specification: Implications for forecasting

模型误设下的结构突变模型及其预测含义

This paper revisits the least squares estimator of the linear regression with a structural break. We view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps. This view is widely held in the forecasting literature and under this view, the time series dependence property of all the observed variables is unstable as well. We establish that the rate of convergence…

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Higher-order improvements of the sieve bootstrap for fractionally integrated processes

分数单整过程筛法 Bootstrap 的高阶改进

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by…

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New tools for understanding the local asymptotic power of panel unit root tests

理解面板单位根检验局部渐近功效的新工具

Motivated by the previously documented discrepancy between actual and predicted power, the present paper provides new tools for analyzing the local asymptotic power of panel unit root tests. These tools are appropriate in general when considering panel data with a dominant autoregressive root of the form ρi=1+ciN−κT−τ, where i=1,…,N indexes the cross-sectional units, T is the number of time periods and ci is a random local-to-unity parameter. A limit theory for the sample…

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Robust standard errors in transformed likelihood estimation of dynamic panel data models with cross-sectional heteroskedasticity

横截面异方差下动态面板变换似然估计的稳健标准误

This paper extends the transformed maximum likelihood approach for estimation of dynamic panel data models by Hsiao et al. (2002) to the case where the errors are cross-sectionally heteroskedastic. This extension is not trivial due to the incidental parameters problem and its implications for estimation and inference. We approach the problem by working with a mis-specified homoskedastic model, and then show that the transformed maximum likelihood estimator continues to be…

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Jackknife model averaging for quantile regressions

分位数回归的刀切法模型平均

In this paper we consider model averaging for quantile regressions (QR) when all models under investigation are potentially misspecified and the number of parameters is diverging with the sample size. To allow for the dependence between the error terms and regressors in the QR models, we propose a jackknife model averaging (JMA) estimator which selects the weights by minimizing a leave-one-out cross-validation criterion function and demonstrate its asymptotic optimality in…

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Large sample properties of the matrix exponential spatial specification with an application to FDI

矩阵指数空间模型的大样本性质及其外国直接投资应用

This paper studies large sample properties of the matrix exponential spatial specification (MESS). We find that the quasi-maximum likelihood estimator (QMLE) for the MESS is consistent under heteroskedasticity, a property not shared by the QMLE of the SAR model. For the general model that has MESS in both the dependent variable and disturbances, labeled MESS(1,1), the QMLE can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two MESS…

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Nonparametric identification and estimation of transformation models

变换模型的非参数识别与估计

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…

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Market-based estimation of stochastic volatility models

随机波动率模型的市场数据估计

We propose a method for estimating stochastic volatility models by adapting the HJM approach to the case of volatility derivatives. We characterize restrictions that observed variance swap dynamics have to satisfy to prevent arbitrage opportunities. When the drift of variance swap rates are affine under the pricing measure, we obtain closed form expressions for those restrictions and formulas for forward variance curves. Using data on the S&P500 index and variance swap rates…

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Quanto option pricing in the presence of fat tails and asymmetric dependence

厚尾与非对称依赖下的定汇率期权定价

We present an approach to pricing European quanto options assuming that the underlying instruments follow a multivariate normal tempered stable (NTS) process. This allows for both fat-tailedness and asymmetric dependence between the returns on the underlying asset and the exchange rate. In an empirical application, we estimate the market and risk-neutral parameters for a quanto construction involving the Nikkei 225 index, as the underlying asset, and the Japanese yen and the…

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Stock return and cash flow predictability: The role of volatility risk

股票收益与现金流可预测性:波动率风险的作用

We examine the joint predictability of return and cash flow within a present value framework, by imposing the implications from a long-run risk model that allow for both time-varying volatility and volatility uncertainty. We provide new evidence that the expected return variation and the variance risk premium positively forecast both short-horizon returns and dividend growth rates. We also confirm that dividend yield positively forecasts long-horizon returns, but that it…

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Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets

异方差ARFIMA模型的分数单整自助得分检验及商品价格应用

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the…

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Empirical evidence on the importance of aggregation, asymmetry, and jumps for volatility prediction

聚合、非对称性与跳跃对波动率预测重要性的实证证据

Many recent modeling advances in finance topics ranging from the pricing of volatility-based derivative products to asset management are predicated on the importance of jumps, or discontinuous movements in asset returns. In light of this, a number of recent papers have addressed volatility predictability, some from the perspective of the usefulness of jumps in forecasting volatility. Key papers in this area include Andersen et al. (2003), Corsi (2004), Andersen et al.…

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COMFORT: A common market factor non-Gaussian returns model

COMFORT:含共同市场因子的非高斯收益模型

A new multivariate time series model with various attractive properties is motivated and studied. By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast EM-algorithm is developed for estimation. Each element of the vector return at time t is endowed with a common…

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A stochastic dominance approach to financial risk management strategies

金融风险管理策略的随机占优比较方法

The Basel III Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one of a range of alternative risk models to forecast Value-at-Risk (VaR). The risk estimates from these models are used to determine the daily capital charges (DCC) and associated capital costs of ADIs, depending in part on the number of previous violations,…

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Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing

用于期权定价的多因子Wishart随机波动率杠杆与反馈效应

The paper proposes a general asymmetric multifactor Wishart stochastic volatility (AMWSV) diffusion process which accommodates leverage, feedback effects and multifactor for the covariance process. The paper gives the closed-form solution for the conditional and unconditional Laplace transform of the AMWSV models. The paper also suggests estimating the AMWSV model by the generalized method of moments using information not only of stock prices but also of realized…

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Pricing with finite dimensional dependence

有限维依赖下的衍生品定价

We consider derivative pricing in factor models, where the factor is Markov with Finite Dimensional Dependence (FDD). The FDD condition allows for explicit formulas for derivative prices and their term structure and in this respect is a serious competitor of models with affine dynamic factors. The approach is illustrated by a comparison of the prices of realized and integrated volatility swaps. We show that the usual practice of replacing a payoff written on the realized…

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A non-linear dynamic model of the variance risk premium

方差风险溢价的非线性动态模型

We propose a new class of non-linear diffusion processes for modeling financial markets data. Our non-linear diffusions are obtained as transformations of affine processes. We show that asset-pricing and estimation is possible and likelihood estimation is straightforward. We estimate a non-linear diffusion model for the VIX index under both the objective measure and the risk-neutral measure where the latter is obtained from futures prices. We find evidence of significant…

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Non-nested testing of spatial correlation

空间相关模型的非嵌套检验

We develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all…

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A flexible semiparametric forecasting model for time series

一种灵活的半参数时间序列预测模型

In this paper, we propose a semiparametric procedure called the “Model Averaging MArginal Regression” (MAMAR) that is flexible for forecasting of time series. This procedure considers approximating a multivariate regression function by an affine combination of one-dimensional marginal regression functions. The weight parameters involved in the approximation are estimated by least squares on the basis of the first-stage nonparametric kernel estimates of the marginal…

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Nonparametric specification tests for stochastic volatility models based on volatility density

基于波动率密度的随机波动率模型非参数设定检验

This paper develops a specification test for stochastic volatility models by comparing the nonparametric kernel deconvolution density estimator of an integrated volatility density with its parametric counterpart. L2 distance is used to measure the discrepancy. The asymptotic null distributions of the test statistics are established and the asymptotic power functions are computed. Through Monte Carlo simulations, the size and power properties of the test statistics are…

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Testing linearity using power transforms of regressors

利用回归变量幂变换检验线性关系

We develop a method of testing linearity using power transforms of regressors, allowing for stationary processes and time trends. The linear model is a simplifying hypothesis that derives from the power transform model in three different ways, each producing its own identification problem. We call this modeling difficulty the trifold identification problem and show that it may be overcome using a test based on the quasi-likelihood ratio (QLR) statistic. More specifically,…

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