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GMM with Weak Identification

弱识别下的广义矩估计

This paper develops asymptotic distribution theory for GMM estimators and test statistics when some or all of the parameters are weakly identified. General results are obtained and are specialized to two important cases: linear instrumental variables regression and Euler equations estimation of the CCAPM. Numerical results for the CCAPM demonstrate that weak-identification asymptotics explains the breakdown of conventional GMM procedures documented in previous Monte Carlo…

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Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation

Technical analysis, also known as “charting,” has been a part of financial practice for many decades, but this discipline has not received the same level of academic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nature of technical analysis—the presence of geometric shapes in historical price charts is often in the eyes of the beholder. In this paper, we propose a systematic and…

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Continuous‐Time Methods in Finance: A Review and an Assessment

金融中的连续时间方法:回顾与评估

I survey and assess the development of continuous‐time methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. During the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance. This latter subperiod has seen…

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Bayesian Dynamic Factor Models and Portfolio Allocation

贝叶斯动态因子模型与投资组合配置

We discuss the development of dynamic factor models for multivariate financial time series, and the incorporation of stochastic volatility components for latent factor processes. Bayesian inference and computation is developed and explored in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The models are direct generalizations of univariate stochastic volatility models and represent specific varieties of…

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Statistical Inference for Random-Variance Option Pricing

随机方差期权定价的统计推断

This article deals with the estimation of continuous-time stochastic volatility models of option pricing. We argue that option prices are much more informative about the parameters than are asset prices. This is confirmed in a Monte Carlo experiment that compares two very simple strategies based on the different information sets. Both approaches are based on indirect inference and avoid any discretization bias by simulating the continuous-time model. We assume an…

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Modelling Stock Market Volatility: Bridging the Gap to Continuous Time

股票市场波动率建模:连接离散时间与连续时间

Understanding And Specifying The Discrete Time Model: D.B. Nelson, Modelling Stock Market Volatility Changes. D.B. Nelson, Stationarity and Persistence in the GARCH(I,I) Model. D.B. Nelson, Conditional Heteroskedasticity in Asset Returns: A New Approach. P.A. Braun, D.B. Nelson and A.M. Sunier, Good News, Bad News, Volatility, and Betas. Continuous Time Limits And Optimal Filtering For ARCH Models: D.B. Nelson, ARCH Models as Diffusion Approximations. D.B. Nelson, Filtering…

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Long-range Dependence in Daily Stock Volatilities

日频股票波动率的长程依赖

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this article, we classify daily stock returns of Standard and Poor 500 companies on the basis of a company's size and its business or industrial…

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Bayesian Analysis of Dynamic Bivariate Mixture Models: Can They Explain the Behavior of Returns and Trading Volume?

动态双变量混合模型的贝叶斯分析:能否解释收益与交易量的行为?

Bivariate mixture models attribute the well-known positive correlation between return volatility and trading volume in financial markets to stochastic changes in a single latent variable representing the number of information arrivals. In this article, dynamic bivariate mixture models that allow for autocorrelation in the latent variable are analyzed by a Bayesian method via Markov-chain Monte Carlo techniques. The results, based on daily data from the Nikkei 225 stock-index…

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Some Econometric Recipes for High-Frequency Data Cooking

高频数据处理的若干计量经济学方法

According to Ragnar Frisch (1933), econometrics involves the mutual penetration of quantitative economic theory and statistical observation. Today, econometric research rarely has all the ingredients spelled out in Frisch's definition. Most econometric models are either very structural, contrived, and unfortunately typically rejected or else they are statistical summaries of stylized data features and unfortunately difficult to link unambiguously to a single theoretical…

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Some Reflections on Analysis of High-Frequency Data

高频数据分析的若干思考

Finance is arguably the most empirically oriented of all the social sciences. This is in part due to the deliberate practical orientation and the ready availability of high-quality financial market data. In recent years, the ever lower costs of data recording and storage have driven the phenomenon to the ultimate limit for some markets: We may have access to time-stamped observations on all quotes and transactions, denoted ultra-high-frequency data by Engle (in press). These…

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Full Bayesian Inference for GARCH and EGARCH Models

GARCH 与 EGARCH 模型的完整贝叶斯推断

A full Bayesian analysis of GARCH and EGARCH models is proposed consisting of parameter estimation, model selection, and volatility prediction. The Bayesian paradigm is implemented via Markov-chain Monte Carlo methodologies. We provide implementation details and illustrations using the General Index of the Athens stock exchange.

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Semiparametric ARCH Models: An Estimating Function Approach

半参数 ARCH 模型:估计函数方法

We introduce the method of estimating functions to study the class of autoregressive conditional heteroscedasticity (ARCH) models. We derive the optimal estimating functions by combining linear and quadratic estimating functions. The resultant estimators are more efficient than the quasi-maximum likelihood estimator. If the assumption of conditional normality is imposed, the estimator obtained by using the theory of estimating functions is identical to that obtained by using…

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Bayesian Portfolio Selection: An Empirical Analysis of the S&P 500 Index 1970–1996

贝叶斯投资组合选择:标普500指数1970—1996年的实证分析

In this article we present a technique for implementing large-scale optimal portfolio selection. We use high-frequency daily data to capture valuable statistical information in asset returns. We describe several statistical issues involved in quantitative approaches to portfolio selection. Our methodology applies to large-scale portfolio-selection problems in which the number of possible holdings is large relative to the estimation period provided by historical data. We…

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Stochastic volatility models: conditional normality versus heavy-tailed distributions

随机波动率模型:条件正态分布与厚尾分布

Most of the empirical applications of the stochastic volatility (SV) model are based on the assumption that the conditional distribution of returns, given the latent volatility process, is normal. In this paper, the SV model based on a conditional normal distribution is compared with SV specifications using conditional heavy-tailed distributions, especially Student's t-distribution and the generalized error distribution. To estimate the SV specifications, a simulated maximum…

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STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

平稳 ARCH 模型:依赖结构与中心极限定理

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

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American options with stochastic dividends and volatility: A nonparametric investigation

随机股息与波动率下的美式期权:非参数研究

In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The…

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The Econometrics of Ultra-high-frequency Data

超高频数据的计量经济学

A complete transactions record is defined to be ultra-high frequency data. The transaction arrival times and associated characteristics can be analyzed by marked point processes. The ACD model developed by Engle and Russell (1998) is then applied to IBM transactions data to develop semi-parametric hazard estimates and measures of conditional variances. Both returns and variances are negatively influenced by surprisingly long durations as suggested by asymmetric information…

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Identifying Bull and Bear Markets in Stock Returns

识别股票收益中的牛市与熊市

This article uses a Markov-switching model that incorporates duration dependence to capture non-linear structure in both the conditional mean and the conditional variance of stock returns. The model sorts returns into a high-return stable state and a low-return volatile state. We label these as bull and bear markets, respectively. The filter identifies all major stock-market downturns in over 160 years of monthly data. Bull markets have a declining hazard function although…

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A Note on Optimal Estimation From a Risk-Management Perspective Under Possibly Misspecified Tail Behavior

尾部行为可能误设时风险管理视角下的最优估计

Many financial time series show leptokurtic behavior--that is, fat tails. Such tail behavior is important for risk management. In this article I focus on the calculation of Value-at-Risk (VaR) as a downside-risk measure for optimal asset portfolios. Using a framework centered on the Student-t distribution, I explicitly allow for a discrepancy between the fat-tailedness of the true distribution of asset returns and that of the distribution used by the investment manager. As a…

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Stock Returns and Dividend Yields Revisited: A New Way to Look at an Old Problem

股票收益与股息收益率再考察:旧问题的新视角

The problem of whether stock returns can he predicted from dividend yields is discussed. I apply a new statistical method for finding reliable confidence intervals for regression parameters in the context of dependent and possibly heteroscedastic data, called subsampling. The method works under very weak conditions and avoids the pitfalls of having to choose a structural model to fit to observed data. Appropriate simulation studies suggest that it has better small-sample…

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