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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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Inference for Generalized Gini Indices Using the Iterated-Bootstrap Method

使用迭代自助法对广义基尼指数进行推断

Inference using the iterated-bootstrap method proposed by Hall is appealing for cases in which the percentile method needs to be used but the nominal level of a confidence interval has to be adjusted. One natural application is for generalized Gini indices of income inequality. When applying these theoretical inequality measures directly to sample data for the purpose of statistical inference, economists must come up with some measure of sampling variation. This is…

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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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The Demand for Lotto: The Role of Conscious Selection

乐透彩票需求:主动选号的作用

This article presents estimates of the elasticity of demand for lottery tickets using time series data in which there is variation in the expected value of a lottery ticket induced by rollovers. An important feature of our data is that there are far more rollovers than expected given the lottery design. We find strong evidence that individuals do not choose their lottery numbers uniformly from a uniform distribution—that is, conscious selection. We use our estimates to…

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Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests

基于平稳性检验的协整系数置信集合

Standard methods for inference in cointegrating systems require all the variables to have exact unit roots and are not at all robust even to slight violations of this condition. In this article, I consider an alternative approach to inference in a cointegrating system. This involves testing the hypothesis that a cointegrating vector takes on a specified value by testing for the stationarity of the associated residual. Confidence sets for the cointegrating vector can be…

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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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Estimating Restricted Cointegrating Vectors

受限协整向量的估计

This article suggests the use of simple minimum-distance methods to estimate restricted cointegrating vectors. The method directly employs minimum-distance methods on unrestricted cointegrating matrices estimated in the usual way to estimate restricted parameters that are linearly or nonlinearly related to the unrestricted cointegrating vector coefficients. The limiting distribution of the estimates and the usual test for the restrictions are derived. A Monte Carlo…

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Efficient Computation of Hierarchical Trends

层级趋势的高效计算

To model a large database containing selling prices for houses, in which local trends, general trends, and specific characteristics play a role, we derived a new procedure to implement a state-space model for repeated measurements. The original model is decomposed into two parts, which are treated differently. The first part is ordinary least squares on data in deviation from means. This step provides a prior for coefficients to be used in the second step, which is a Kalman…

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Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence

自回归模型中基于残差的正态性检验:渐近理论与模拟证据

Existing results for the asymptotic validity of the Jarque-Bera test in vector autoregressive (VAR) models assume stationarity. In applied work, however, researchers often work with possibly integrated and cointegrated process. We prove the asymptotic validity of the Jarque-Bera test for vector error-correction (VEC) models and for unrestricted VAR models with possibly integrated or cointegrated variables. We also propose the use of bootstrap critical values in stationary…

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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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Strongly Consistent Determination of Cointegrating Rank Via Canonical Correlations

基于典型相关的协整秩强一致判定

This article is concerned with the statistical analysis of nonstationary, cointegrated time series. The estimation of the cointegrating structure of such time series is considered, and the problem of identifying the cointegrating rank is addressed. A methodology is presented that leads to strongly consistent estimates of this quantity. The identification is based on a canonical correlation analysis of the original variables and presents an alternative approach to those…

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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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Alternative Variance-Ratio Tests Using Ranks and Signs

基于秩与符号的替代方差比检验

This article proposes using variance-ratio tests based on the ranks and signs of a time series to test the null that the series is a martingale difference sequence. Unlike conventional variance-ratio tests, these tests can be exact. In Monte Carlo simulations, I find that they can also be more powerful than conventional variance-ratio tests. I apply the proposed tests to five exchange-rate series and find that they are capable of detecting violations of the martingale…

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Bayesian Unit-Root Testing in Stochastic Volatility Models

随机波动率模型中的贝叶斯单位根检验

This article uses a Bayesian unit-root test in stochastic volatility models. The time series of interest is the volatility that is unobservable. The unit-root testing is based on the posterior odds ratio, which is approximated by Markov-chain Monte Carlo methods. Simulations show that the testing procedure is efficient for moderate sample size. The unit-root hypothesis is rejected in seven market indexes, and some evidence of nonstationarity is observed in the TWSI of Taiwan.

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CoSmo: A Constrained Scatterplot Smoother for Estimating Convex, Monotonic Transformations

CoSmo:估计凸性与单调变换的约束散点平滑方法

In many of the applied sciences, it is common that the forms of empirical relationships are almost completely unknown prior to study. Scatterplot smoothers used in nonparametric regression methods have considerable potential to ease the burden of model specification that a researcher would otherwise face in this situation. Occasionally the researcher will know the sign of the first or second derivatives, or both. This article develops a smoothing method that can incorporate…

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Nonlinear Predictability of Stock Returns Using Financial and Economic Variables

利用金融与经济变量预测股票收益的非线性方法

Inspired by the linear predictability and nonlinearity found in the finance literature, this article examines the nonlinear predictability of the excess returns. The relationship between the excess returns and the predicting variables is recursively modeled by a neural-network model, which is capable of performing flexible nonlinear functional approximation. The nonlinear neural-network model is found to have better in-sample fit and out-of-sample forecasts compared to its…

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Testing Symmetry and Proportionality in PPP: A Panel-Data Approach

购买力平价中对称性与比例性的面板检验

Purchasing power parity (PPP) is a proposition equating the nominal exchange rate to the ratio of the domestic to foreign price levels. This article employs Bayesian panel-data methods to test for PPP, in particular, the implied symmetry and proportionality conditions. Using a dataset of all the Organization for Economic Cooperation and Development member countries in the post-Bretton Woods era, I do not find support for symmetry and proportionality in PPP over time and…

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Limit Moves as Censored Observations of Equilibrium Futures Price in GARCH Processes

将涨跌停视为均衡期货价格删失观测的 GARCH 估计

We develop an algorithm for estimating generalized autoregressive conditional heteroscedasticity models for time series containing some censored observations. Motivation for the algorithm comes from those futures markets and some equity markets that have limits constraining the maximum allowable movement in price in a day. When a limit is reached, trading stops and the equilibrium price is not observed. We maximize the likelihood function by replacing the unobservable…

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Forecasting With Stable Seasonal Pattern Models With an Application to Hawaiian Tourism Data

稳定季节模式模型的预测:夏威夷旅游数据应用

We propose several variations of the stable seasonal pattern (SSP) model first introduced by Marshall and Oliver and study their prediction procedures. Depending on the type of data (count data or continuous variable), we propose different treatments. Previously SSP models have been applied to trendless data or adapted to trending data in ad hoc ways. In the models considered here, conditional independence allows the seasonal pattern and trend to be modeled separately,…

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