The stochastic volatility in mean model: empirical evidence from international stock markets

In this paper we present an exact maximum likelihood treatment for the estimation of a Stochastic Volatility in Mean (SVM) model based on Monte Carlo simulation methods. The SVM model incorporates the unobserved volatility as an explanatory variable in the mean equation. The same extension is developed elsewhere for Autoregressive Conditional Heteroscedastic (ARCH) models, known as the ARCH in Mean (ARCH‐M) model. The estimation of ARCH models is relatively easy compared with that of the Stochastic Volatility (SV) model. However, efficient Monte Carlo simulation methods for SV models have been developed to overcome some of these problems. The details of modifications required for estimating the volatility‐in‐mean effect are presented in this paper together with a Monte Carlo study to investigate the finite sample properties of the SVM estimators. Taking these developments of estimation methods into account, we regard SV and SVM models as practical alternatives to their ARCH counterparts and therefore it is of interest to study and compare the two classes of volatility models. We present an empirical study of the intertemporal relationship between stock index returns and their volatility for the United Kingdom, the United States and Japan. This phenomenon has been discussed in the financial economic literature but has proved hard to find empirically. We provide evidence of a negative but weak relationship between returns and contemporaneous volatility which is indirect evidence of a positive relation between the expected components of the return and the volatility process. Copyright © 2002 John Wiley & Sons, Ltd.     

Generalized R-estimators under conditional heteroscedasticity

In this paper, we extend the classical idea of Rank estimation of parameters from homoscedastic problems to heteroscedastic problems. In particular, we define a class of rank estimators of the parameters associated with the conditional mean function of an autoregressive model through a three-steps procedure and then derive their asymptotic distributions. The class of models considered includes Engel's ARCH model and the threshold heteroscedastic model. The class of estimators includes an extension of Wilcoxon-type rank estimator. The derivation of the asymptotic distributions depends on the uniform approximation of a randomly weighted empirical process by a perturbed empirical process through a very general weight-dependent partitioning argument.     

Modelling multi‐period inflation uncertainty using a panel of density forecasts

This paper examines the determinants of inflation forecast uncertainty using a panel of density forecasts from the Survey of Professional Forecasters (SPF). Based on a dynamic heterogeneous panel data model, we find that the persistence in forecast uncertainty is much less than what the aggregate time series data would suggest. In addition, the strong link between past forecast errors and current forecast uncertainty, as often noted in the ARCH literature, is largely lost in a multi‐period context with varying forecast horizons. We propose a novel way of estimating ‘news’ and its variance using the Kullback‐Leibler information, and show that the latter is an important determinant of forecast uncertainty. Our evidence suggests a strong relationship of forecast uncertainty with level of inflation, but not with forecaster discord or with the volatility of a number of other macroeconomic indicators. Copyright © 2006 John Wiley & Sons, Ltd.     

Structural analysis of portfolio risk using beta impulse response functions

We estimate the data generating process of daily excess returns of 20 major German stocks in a CAPM framework with time varying betas. Our sample spans a 23 year period from 1974 to 1996. An asymmetric dependence of volatility on lagged innovations is taken into account. We introduce beta impulse response functions to shed light on the structural implications of systematic risk associated with competing volatility models. The dependence of beta on news is characterized with respect to different sources (asset specific vs. market general news). The empirical results suggest that negative news emerging from the market involve a stronger impact on beta relative to positive news. Concerning firm specific news the opposite relation is found for the majority of the analysed data sets.     

沪深股市在牛市和熊市阶段的波动非对称效应实证分析

本文分别采用EGARCH-M、TGARCH-M模型对沪深股市在牛市和熊市阶段的非对称波动效应进行了分析,这两个模型得出了相同的结论,在牛市阶段利好消息引起股市更大的波动,在熊市阶段利空消息引起股市更大的波动,而且这两个模型同时也说明了我国股市风险和收益的正相关关系,并从我国股票市场交易者构成和交易机制两方面说明了波动非对称的原因。     

Conditional heteroscedasticity of exchange rates: further results based on the fractionally integrated approach

A recent article (Tse, 1998 ) published in this journal analysed the conditional heteroscedasticity of the yen–dollar exchange rate based on the fractionally integrated asymmetric power ARCH model. In this paper, we present replication results using Tse's ( 1998 ) yen–dollar series. We also examine the robustness of Tse's ( 1998 ) findings across different currencies, sample periods and non‐nested GARCH‐type models. Unlike Tse ( 1998 ), we find some evidence of asymmetric conditional volatility for daily returns of currencies measured against the dollar or the yen. Copyright © 2004 John Wiley & Sons, Ltd.     

A Portfolio Index GARCH model

This paper develops the structure of a parsimonious Portfolio Index (PI) GARCH model. Unlike the conventional approach to Portfolio Index returns, which employs the univariate ARCH class, the PI-GARCH approach incorporates the effects on individual assets, leading to a better understanding of portfolio risk management, and achieves greater accuracy in forecasting Value-at-Risk (VaR) thresholds. For various asymmetric GARCH models, a Portfolio Index Composite News Impact Surface (PI-CNIS) is developed to measure the effects of news on the conditional variances. The paper also investigates the finite sample properties of the PI-GARCH model. The empirical example shows that the asymmetric PI-GARCH-t model outperforms the GJR-t model and the filtered historical simulation with a t distribution in forecasting VaR thresholds.     

Information flows and stock market volatility

This study examines how news is distributed across stocks. A model is developed that categorizes a stock's latent news into normal and nonnormal news, and allows both types of news to be filtered through to other stocks. This is achieved by formulating a model that jointly incorporates a multivariate lognormal‐Poisson jump process (for nonnormal news) and a multivariate GARCH process (for normal news), in addition to a news (or shock) transmission mechanism that allows the shocks from both processes to impact intertemporally on all stocks in the system. The relationship between news and the expected volatility surface is explored and a unique news impact surface is derived that depends on time, news magnitude, and news type. We find that the effect of nonnormal news on volatility expectations typically builds up before dissipating, with the news transmission mechanism effectively crowding‐out normal news and crowding‐in nonnormal news. Moreover, in contrast to the standard approach for measuring leverage effects using asymmetric generalized autoregressive conditional heteroskedasticity models, we find that leverage effects stem predominantly from nonnormal news. Finally, we find that the capacity to identify positively or negatively correlated stock returns is ambiguous in the short term, and depends heavily on the behavior of the nonnormal news component.     

我国股市波动的阶段性特征研究——基于ARCH模型族的实证研究

以上证综合指数为代表,根据我国股市交易制度的两次转变,把我国股市自1991年至2006年的15年发展历程分为三个阶段,利用ARCH族模型,从股市波动的集聚性、持续性、"杠杆效应"几个方面,研究了我国股市15年间的波动特征的变迁,得出了一些富有现实意义的结论。     

ARCH MODELS: PROPERTIES, ESTIMATION AND TESTING

Abstract. The aim of this survey paper is to provide an account of some of the important developments in the autoregressive conditional heteroskedasticity (ARCH) model since its inception in a seminal paper by Engle (1982). This model takes account of many observed properties of asset prices, and therefore, various interpretations can be attributed to it. We start with the basic ARCH models and discuss their different interpretations. ARCH models have been generalized in different directions to accommodate more and more features of the real world. We provide a comprehensive treatment of many of the extensions of the original ARCH model. Next we discuss estimation and testing for ARCH models and note that these models lead to some interesting and unique problems. There have been numerous applications and we mention some of these as we present different models. The paper includes a glossary of the acronyms for the models we describe.     

资产收益率跳扩散过程的混频数据估计：一个波动率回馈框架

本文提出一个利用混频数据估计资产波动率的框架,该框架使用日内高频数据构造蕴含潜在发生概率的跳跃和扩散波动指标,以外生的滞后项进入回馈函数,既能充分利用样本信息,又能避免无限滞后期的回馈影响。在对沪深300指数的实证分析中,考虑一个跳跃对扩散波动具有非对称性溢出效应的双向波动率回馈模型。相对于基准模型,这一模型对数据的描述更优。分析结果显示,两类波动间存在正向回馈效应：跳跃向扩散的溢出导致自回归条件异方差（ARCH）系数存在两个区制且区制内的变异性明显;扩散向跳跃的溢出致使跳跃强度的自相关性在极端市场环境中出现强化。波动率回馈机制使得信息释放后价格反复调整变化,导致波动率高企;熔断事件折射出A股信息流质量差、融解效率低等问题。由此可以得出结论：相关监管和交易制度亟待完善。     

An empirical analysis of alternative parametric ARCH models

This paper presents empirical evidence on the effectiveness of eight different parametric ARCH models in describing daily stock returns. Twenty‐seven years of UK daily data on a broad‐based value weighted stock index are investigated for the period 1971–97. Several interesting results are documented. Overall, the results strongly demonstrate the utility of parametric ARCH models in describing time‐varying volatility in this market. The parameters proxying for asymmetry in models that recognize the asymmetric behaviour of volatility are highly significant in each and every case. However, the ‘performance’ of the various parameterizations is often fairly similar with the exception of the multiplicative GARCH model that performs qualitatively differently on several dimensions of performance. The outperformance of any model(s) is not consistent across different sub‐periods of the sample, suggesting that the optimal choice of a model is period‐specific. The outperformance is also not consistent as we change from in‐sample inferences to out‐of‐sample inferences within the same period. Copyright © 2000 John Wiley & Sons, Ltd.     

How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches

This paper examines the dynamic relationship between firm-level return volatility and public news sentiment. By using the new RavenPack News Analytics ⿿ Dow Jones Edition database that captures over 1200 types of firm-specific and macroeconomic news releases and their sentiment scores at high frequencies, we investigate the circumstances in which public news sentiment is related to the intraday volatility of the constituent stocks in the Dow Jones Composite Average (DJN 65). Two different conditionally heteroskedastic models are employed: the Fractionally Integrated Generalized Autoregressive Conditionally Heteroskedastic (FIGARCH) and the two-state Markov Regime-Switching GARCH (RS-GARCH) models. For most of the DJN 65 stocks, our results confirm the significant impact of firm-specific news sentiment on intraday volatility persistence, even after controlling for the potential effects of macroeconomic news. Compared with macroeconomic news sentiment, firm-specific news sentiment apparently accounts for a greater proportion of overall volatility persistence. Moreover, negative news has a greater impact on volatility than positive news. Furthermore, the results from the RS-GARCH model indicate that news sentiment accounts for a greater proportion of volatility persistence in the high-volatility regime (turbulent state) than in the low-volatility regime (calm state). In-sample forecasting performance and residual diagnostic tests suggest that FIGARCH generally outperforms RS-GARCH.     

Stochastic volatility with leverage: Fast and efficient likelihood inference

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).     

Media Content,Accounting Quality,and Liquidity Volatility

We examine how the linguistic content of news items affects the volatility of a firm's liquidity, and we consider whether accounting quality moderates the media content-liquidity volatility relation. Regarding the unconditional relation between media content and liquidity volatility, one view is media content could reduce liquidity volatility by providing additional information about fundamental values; another view is it could increase liquidity volatility by increasing investor uncertainty, particularly for negative news. Using data from Thomson Reuters News Analytics, we find evidence supporting the view that media content, positive and negative, has incremental information. Regarding the moderating role of accounting quality, pre-existing accounting information of higher quality could enhance investors' reactions to media content by providing a more precise baseline, or it could reduce investors' reactions to the news if investors anchor on higher quality financial statements. Our findings are consistent with more credible accounting information serving an anchor role, and suggest that investors condition their reaction to media content based on the quality of a firm's pre-existing accounting information.     

Temporal aggregation of volatility models

In this paper, we consider temporal aggregation of volatility models. We introduce semiparametric volatility models, termed square-root stochastic autoregressive volatility (SR-SARV), which are characterized by autoregressive dynamics of the stochastic variance. Our class encompasses the usual GARCH models and various asymmetric GARCH models. Moreover, our stochastic volatility models are characterized by multiperiod conditional moment restrictions in terms of observables. The SR-SARV class is a natural extension of the class of weak GARCH models. This extension has four advantages: (i) we do not assume that fourth moments are finite; (ii) we allow for asymmetries (skewness, leverage effect) that are excluded from weak GARCH models; (iii) we derive conditional moment restrictions and (iv) our framework allows us to study temporal aggregation of IGARCH models.     

The relationship between forecast dispersion and forecast uncertainty: Evidence from a survey data—arch model

This paper examines empirically the relationship between measures of forecast dispersion and forecast uncertainty from data on inflation expectations from the Livingston survey series and the Survey Research Center (SRC) survey series. Because the survey series do not provide probabilistic forecasts of inflation, we derive measures of inflation uncertainty by modelling the conditional variance of the inflation forecast errors from the survey series as an autoregressive conditional heteroscedastic (ARCH) process. The analysis is complicated by the fact that the overlap of forecast horizons for the survey series does not preclude the model's disturbance terms from displaying autocorrelation, and also places a restriction on the specification for the ARCH measures of inflation uncertainty. We estimate the model using Hansen's (1982) generalized method of moments (GMM) procedure to account for the presence of serial correlation and conditional heteroscedasticity in the disturbance terms. The results generally support the hypothesis that the measures of forecast dispersion across survey respondents are positively and statistically significantly associated with the measures of inflation uncertainty. However, the appropriateness of using forecast dispersion measures as proxies for inflation uncertainty is sensitive to the choice of the survey series.     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

Inconsistency of the MLE and inference based on weighted LS for LARCH models

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. Their performance is illustrated via simulation experiments. It is also investigated whether stock market returns exhibit some of the characteristic features of the linear ARCH model.