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A Comment on: “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data”

评《自回归条件持续时间:不规则间隔交易数据的新模型》

Based on the GARCH literature, Engle and Russell (1998) established consistency and asymptotic normality of the QMLE for the autoregressive conditional duration (ACD) model, assuming strict stationarity and ergodicity of the durations. Using novel arguments based on renewal process theory, we show that their results hold under the stronger requirement that durations have finite expectation. However, we demonstrate that this is not always the case under the assumption of…

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A Sieve‐SMM Estimator for Dynamic Models

动态模型的筛模拟矩估计量

This paper proposes a Sieve Simulated Method of Moments (Sieve‐SMM) estimator for the parameters and the distribution of the shocks in nonlinear dynamic models where the likelihood and the moments are not tractable. An important concern with SMM, which matches sample with simulated moments, is that a parametric distribution is required. However, economic quantities that depend on this distribution, such as welfare and asset prices, can be sensitive to misspecification. The…

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Macro‐Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models

宏观—金融解耦:宏观资产定价模型的稳健评估

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including (time‐varying) rare‐disaster risk models and long‐run risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a…

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A ReMeDI for Microstructure Noise

ReMeDI:微观结构噪声的分离增量已实现矩方法

We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high‐frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed…

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When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility

移动平均模型与高频数据:波动率的一致有效推断

We conduct inference on volatility with noisy high‐frequency data. We assume the observed transaction price follows a continuous‐time Itô‐semimartingale, contaminated by a discrete‐time moving‐average noise process associated with the arrival of trades. We estimate volatility, defined as the quadratic variation of the semimartingale, by maximizing the likelihood of a misspecified moving‐average model, with its order selected based on an information criterion. Our inference…

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Reply to “Rational Bubbles in UK Housing Markets”

对《英国住房市场中的理性泡沫》的回应

In Giglio, Maggiori, and Stroebel (2016), we propose and implement a new test for classic rational bubbles. Such bubbles derive their value from each agent's rational expectation of being able to resell the bubble claims to the next agent. Backward induction ensures that classic rational bubbles can only exist on infinite‐maturity assets. Our empirical exercise shows that infinite‐maturity claims and 999‐year claims for otherwise identical housing assets trade at the same…

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Realized Semicovariances

We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results…

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Identifying Long-Run Risks: A Bayesian Mixed-Frequency Approach

长期风险识别:贝叶斯混频方法

We document that consumption growth rates are far from i.i.d. and have a highly persistent component. First, we estimate univariate and multivariate models of cash‐flow (consumption, output, dividends) growth that feature measurement errors, time‐varying volatilities, and mixed‐frequency observations. Monthly consumption data are important for identifying the stochastic volatility process; yet the data are contaminated, which makes the inclusion of measurement errors…

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Nonparametric Stochastic Discount Factor Decomposition

随机折现因子的非参数分解

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009). Our empirical framework…

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Spurious Inference in Reduced-Rank Asset-Pricing Models

降秩资产定价模型中的虚假推断

We study some seemingly anomalous results that arise in possibly misspecified, reduced-rank linear asset-pricing models estimated by the continuously updated generalized method of moments. When a spurious factor (that is, a factor that is uncorrelated with the returns on the test assets) is present, the test for correct model specification has asymptotic power that is equal to the nominal size. In other words, applied researchers will erroneously conclude that the model is…

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Statistical Properties of Microstructure Noise

微观结构噪声的统计性质

We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, and the noise to be dependent on the price process and to have diurnal features. Estimators of arbitrary orders of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In…

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Jump Regressions

跳跃回归

We develop econometric tools for studying jump dependence of two processes from high‐frequency observations on a fixed time interval. In this context, only segments of data around a few outlying observations are informative for the inference. We derive an asymptotically valid test for stability of a linear jump relation over regions of the jump size domain. The test has power against general forms of nonlinearity in the jump dependence as well as temporal instabilities. We…

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Long-Term Risk: A Martingale Approach

长期风险:鞅方法

This paper extends the long-term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discrete-time ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends…

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Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

高频数据的不确定性评估:观测渐近方差

The availability of high frequency financial data has generated a series of estimators based on intra-day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the…

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Generalized Method of Integrated Moments for High-Frequency Data

高频数据的广义积分矩方法

We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator…

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Time-Varying Risk Premium in Large Cross-Sectional Equity Data Sets

大型股票横截面数据中的时变风险溢价

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time-varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset-specific instruments. The estimator uses simple weighted two-pass cross-sectional regressions, and we show its consistency and asymptotic normality under increasing…

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Parametric Inference and Dynamic State Recovery From Option Panels

基于期权面板的参数推断与动态状态恢复

We develop a new parametric estimation procedure for option panels observed with error. We exploit asymptotic approximations assuming an ever increasing set of option prices in the moneyness (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for…

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Power Enhancement in High-Dimensional Cross-Sectional Tests

高维横截面检验的功效增强

= 0 against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high-dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme-value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often…

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Local Identification of Nonparametric and Semiparametric Models

非参数与半参数模型的局部识别

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification.…

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Testing for Common Conditionally Heteroskedastic Factors

共同条件异方差因子的检验

This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features property is expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter value and therefore the standard asymptotic results of Hansen (1982) do not apply. We show in this context that Hansen's (1982) J-test…

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Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local-to-Continuity Theory for the Pre-Averaging Method

含噪高频数据中跳跃的稳健估计与推断:预平均方法的局部趋于连续理论

We develop an asymptotic theory for the pre-averaging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple bias-corrected estimators for jump power variations, and construct robust…

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Alpha as Ambiguity: Robust Mean-Variance Portfolio Analysis

作为模糊性的 Alpha:稳健均值—方差投资组合分析

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as de…ned by the smooth model of decision making under ambiguity of Klibano¤, Marinacci and Mukerji (2005).We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty.In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we …nd that portfolio rebalancing in response to…

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The Realized Laplace Transform of Volatility

波动率的已实现拉普拉斯变换

We introduce and derive the asymptotic behavior of a new measure constructed from high-frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long-span and infill asymptotics, the…

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Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression

利用非参数回归检验时间序列模型的平滑结构变化

Checking parameter stability of econometric models is a long-standing problem. Almost all existing structural change tests in econometrics are designed to detect abrupt breaks. Little attention has been paid to smooth structural changes, which may be more realistic in economics. We propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points. The idea is to estimate smooth time-varying parameters by local…

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