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Reading the Candlesticks: An OK Estimator for Volatility

解读 K 线:即时波动率的 OK 估计量

Abstract We propose an Optimal candlesticK (OK) estimator for the spot volatility using high-frequency candlestick observations. Under a standard infill asymptotic setting, we show that the OK estimator is asymptotically unbiased and has minimal asymptotic variance within a class of linear estimators. Its estimation error can be coupled by a Brownian functional, which permits valid inference. Our theoretical and numerical results suggest that the proposed candlestick-based…

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Robust Inference in Models Identified via Heteroskedasticity

通过异方差识别的模型中的稳健推断

Abstract Identification via heteroskedasticity exploits variance changes between regimes to identify parameters in simultaneous equations. Weak identification occurs when shock variances change very little or multiple variances change close to proportionally, making standard inference unreliable. I propose an F-test for weak identification in a common simple version of the model. More generally, I establish conditions for validity of nonconservative robust inference on…

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Characteristic-Sorted Portfolios: Estimation and Inference

按特征排序的投资组合:估计与推断

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of…

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Determining the Number of Factors from Empirical Distribution of Eigenvalues

利用特征值经验分布确定因子数

We develop a new estimator of the number of factors in the approximate factor models. The estimator works well even when the idiosyncratic terms are substantially correlated. It is based on the fact, established in the paper, that any finite number of the largest "idiosyncratic" eigenvalues of the sample covariance matrix cluster around a single point. In contrast, all the "systematic" eigenvalues, the number of which equals the number of factors, diverge to infinity. The…

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Nonstationarities in Stock Returns

股票收益的非平稳性

The paper outlines a methodology for analyzing daily stock returns that relinquishes the assumption of global stationarity. Giving up this common working hypothesis reflects our belief that fundamental features of the financial markets are continuously and significantly changing. Our approach approximates the nonstationary data locally by stationary models. The methodology is applied to the S&P 500 series of returns covering a period of over seventy years of market activity.…

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Inference on Predictability of Foreign Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models

利用广义谱与非线性时间序列模型推断汇率可预测性

It is often documented, based on autocorrelation, variance ratio, and power spectrum, that exchange rates approximately follow a martingale process. Because these data check serial uncorrelatedness rather than martingale difference, they may deliver misleading conclusions in favor of the martingale hypothesis when the test statistics are insignificant. In this paper, we explore whether there exists a gap between serial uncorrelatedness and martingale difference for exchange…

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Inference on Predictability of Foreign Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models

利用广义谱与非线性时间序列模型推断汇率可预测性

It is often documented, based on autocorrelation, variance ratio, and power spectrum, that exchange rates approximately follow a martingale process. Because these data check serial uncorrelatedness rather than martingale difference, they may deliver misleading conclusions in favor of the martingale hypothesis when the test statistics are insignificant. In this paper, we explore whether there exists a gap between serial uncorrelatedness and martingale difference for exchange…

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Flexible Multivariate GARCH Modeling with an Application to International Stock Markets

灵活的多元GARCH建模及其在国际股票市场中的应用

This paper offers a new approach to estimating time-varying covariance matrices in the framework of the diagonal-vech version of the multivariate GARCH(1,1) model. Our method is numerically feasible for large-scale problems, produces positive semidefinite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator with a number of…

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Testing Parametric Conditional Distributions of Dynamic Models

动态模型参数化条件分布的检验

This paper proposes a nonparametric test for parametric conditional distributions of dynamic models. The test is of the Kolmogorov type coupled with Khmaladze's martingale transformation. It is asymptotically distribution-free and has nontrivial power against root-n local alternatives. The method is applicable for various dynamic models, including autoregressive and moving average models, generalized autoregressive conditional heteroskedasticity (GARCH), integrated GARCH,…

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Semiparametric Weak-Instrument Regressions with an Application to the Risk-Return Tradeoff

半参数弱工具变量回归及其风险—收益权衡应用

We extend the local-to-zero analysis of models with weak instruments to models with estimated instruments and regressors and with higher-order dependence between instruments and disturbances. This framework is applicable to linear models with expectation variables that are estimated nonparametrically, such as the risk-return tradeoff in finance and the effect of inflation uncertainty on real economic activity. Our simulation evidence suggests that Lagrange multiplier…

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Real-Exchange-Rate Uncertainty and Private Investment in LDCS

发展中国家的实际汇率不确定性与私人投资

This paper examines empirically the link between real-exchange-rate uncertainty and private investment in developing countries, using a large cross-country time series data set. The paper builds a GARCH-based measure of real-exchange-rate volatility and finds that it has a strong negative effect on investment, after controlling for other standard investment determinants and taking into account their potential endogeneity. The effect of uncertainty is not uniform, however.…

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Multifractality in Asset Returns: Theory and Evidence

资产收益的多重分形:理论与证据

This paper investigates the multifractal model of asset returns (MMAR), a class of continuous-time processes that incorporate the thick tails and volatility persistence exhibited by many financial time series. The simplest version of the MMAR compounds a Brownian motion with a multifractal time-deformation. Prices follow a semi-martingale, which precludes arbitrage in a standard two-asset economy. Volatility has long memory, and the highest finite moments of returns can take…

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Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance

利用日内极差校准波动率扩散并提取远期积分方差

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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Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data

Many panel data sets encountered in macroeconomics, international economics, regional science, and finance are characterized by cross-sectional or "spatial" dependence. Standard techniques that fail to account for this dependence will result in inconsistently estimated standard errors. In this paper we present conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very…

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The Fisher Effect and the Term Structure of Interest Rates: Tests of Cointegration

费雪效应与利率期限结构:协整检验

The literature on the Fisher effect has ignored the potential relationship between inflation and long-term interest rates. Using an expectations model of the term structure of interest rates, the authors establish the conditions under which innovations in short-term inflation will be transmitted to long-term as well as short-term interest rates. Cointegration tests find support for both the Fisher effect and the expectations theory of the term structure. Copyright 1993 by…

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