Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

人民币汇率与股市收益的动态关联性实证研究

利用基于广义误差分布（GED）的多因素TGARCH模型,实证分析了2005年7月21日汇改后人民币汇率与中国股市收益的动态关系。估计结果显示：人民币汇率对股市收益有显著的价格扩散效应,汇率上升会引起上证指数收益率较大幅度的上升;股市收益波动存在显著的ARCH效应和GARCH效应,并且等强度的正向或负向新息的冲击会引起股市波动的非对称反应,正向冲击比同强度的负向冲击能带来股市更大的未来波动。     

Asymmetry, realised volatility and stock return risk estimates

In this paper we estimate minimum capital risk requirements for short and long positions with three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes. We also address the problem of the extremely high estimated persistence of the GARCH model to generate observed volatility patterns by including realised volatility as an explanatory variable into the model??s variance equation. The results suggest that the inclusion of realised volatility improves the GARCH forecastability as well as its ability to calculate accurate minimum capital risk requirements and makes it quite competitive when compared with asymmetric conditional heteroscedastic models such as the GJR and the EGARCH.     

中国通货膨胀率及其波动关系分析

有关通货膨胀率和通货膨胀率波动影响关系,存在F riedm an-B a ll和Cuk ierm an-M e ltzer两种假说,即存在通货膨胀率及其波动的相互影响关系。使用GARCH和TGARCH模型,选择中国1993~2004年月度通货膨胀率数据,检验结果表明F riedm an-B a ll假说成立,稳健的货币政策对经济发展有积极作用。     

Predictive ability of asymmetric volatility models at medium-term horizons

Using realized volatility to estimate conditional variance of financial returns, we compare forecasts of volatility from linear GARCH models with asymmetric ones. We consider horizons extending to 30 days. Forecasts are compared using three different evaluation tests. With data from an equity index and two foreign exchange returns, we show that asymmetric models provide statistically significant forecast improvements upon the GARCH model for two of the datasets and improve forecasts for all datasets by means of forecasts combinations. These results extend to about 10 days in the future, beyond which the forecasts are statistically inseparable from each other.     

On nonlinear dependencies in African stock markets

Ferreira, Dionisio, and Correia (2018. Physica A: Statistical Mechanics and Its Applications. 505, 680–687) showed that African stock markets at different time frames (before the Lehman Brothers financial crisis, during the crisis, and after the crisis) do not satisfy the efficient market hypothesis. Here, we provide evidence by means of six different nonparametric tests, and the fit of GARCH(1, 1), TGARCH(1, 1) and EGARCH(1, 1) models accounting for day of the week and month of the year effects that the majority of African stock markets do comply with the efficient market hypothesis.     

ASYMMETRIC INFORMATION IMPACTS: EVIDENCE FROM THE AUSTRALIAN TREASURY-BOND FUTURES MARKET

Abstract.  The effect of information flows on the return volatility of Australian 3-year Treasury bond futures is examined using linear and non-linear GARCH models. Results show significant asymmetric information effects, where bad news has a greater impact on volatility than good news and a non-linear Threshold ARCH(1,1) in mean model provides the most accurate estimation of return volatility. Diagnostic tests confirm this finding and out of sample forecasting error statistics verify that the Threshold ARCH(1,1) in mean model yields the lowest forecasting error. The Threshold ARCH(1,1)-M model is best at capturing the asymmetric information impact on the Australian three-year T-Bond futures return volatility.     

Finite-sample size distortion of the AESTAR unit root test: GARCH,corrected variance–covariance matrix estimators and adjusted critical values

The behaviour of the asymmetric exponential smooth transition autoregressive (AESTAR) unit root test, which allows for asymmetric and nonlinear reversion to equilibrium, is examined in the presence of generalized autoregressive conditional heteroscedasticity (GARCH). It is found that while the test is relatively robust in the presence of ‘low volatility’ GARCH processes, it exhibits substantial size distortion when large values of the volatility parameter are considered. Attempted resolution via the routine application of heteroscedasticity consistent (or ‘corrected’) covariance matrix estimators (HCCMEs) is shown to result in overwhelming size distortion due to their impact upon the finite-sample distribution of the underlying test statistic. However, application of a corrected HCCME, in combination with critical values derived specifically under its use, results in the control of test size. Analogous results for the Dickey–Fuller (1979) test are presented to permit comparison with a test considering linear, symmetric adjustment. It is found that the AESTAR test is subject to far greater distortion than its linear, symmetric alternative. In summary, the results indicate that caution must be exercised when applying the AESTAR test to macroeconomic and financial time series, particularly if routine application of corrected covariance matrix estimators occurs.     

Trading asymmetric trend and volatility by leverage trend GARCH in Taiwan stock index

This article develops a leverage trend Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model by incorporating asymmetric trend of returns of the exponential autoregressive and asymmetric volatility of GARCH models to study the asymmetric effects. Using in-sample daily data of Taiex over the period 4 January 1980 to 25 August 1997 and postsample daily data over the period 26 August 1997 to 10 September 2007, the evidence reveals that a curvaceous risk–return relationship and both asymmetric volatility and asymmetric trend of returns are significant in Taiex. The episode of asymmetric trend of returns is that the positive information creates a higher return trend than the negative information of the same amount, while similarly to most studies, the evidence of asymmetric volatility appears that the negative information makes a higher volatility than the positive information of the same size. Most remarkably, we evidence that the volatility asymmetry effect is a conservative trading factor and the return trend asymmetry effect is an active trading factor. In comparison of post-sample performance using rolling-window technique, the leverage trend GARCH model indeed outperforms the other three models with single asymmetry adjusted or without asymmetry adjusted, while the asymmetry nonadjusted model performs the worst. It implies that the return trend asymmetry (active trading) and the volatility asymmetry effects (conservative trading) tend to compensate, but not offset each other.     

Nonlinear dynamics: Evidence for a small stock exchange

This paper models the main stock index of the Vienna Stock Exchange with daily data from 1986 to 1992. We find that returns are nonnormal and show linear and nonliner dependence. On that basis we compare the fit of alternative specifications of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) to the Markov-Switching approach. The models are evaluated with diagnostic tests on the standardized residuals. We consider evidence for deterministic structures and for infinite variance. Our main result is that a parsimonious model from the GARCH – class can generate the statistical properties of daily returns. The behavior of the two types of models with respect to temporal aggregation is found to differ significantly. First version received: January 1996/Final version received: December 1997     

Can asymmetric conditional volatility imply asymmetric tail dependence?

In this article, we investigate two types of asymmetries, that is, the asymmetry of conditional volatility and the asymmetry of tail dependence in the crude oil markets. We employ the two different sample datasets in which each dataset covers the time period of stable and unstable oil prices, individually. A variety of different copulas and three asymmetric GARCH regression models are used in order to capture the two types of asymmetries. In particular, we extend the TBL-GARCH model proposed by Choi et al. (2012) to the asymmetric GARCH regression type model. The findings from the two different approaches are congruent, in that there is no asymmetry of tail dependence and no asymmetric conditional volatility in crude oil returns over the two different sample periods. Our study reconfirms the findings of Aboura and Wagner (2016) by showing that asymmetric conditional volatility relates to asymmetric tail dependence.     

基于GARCH模型对人民币汇率波动的实证研究

本文建立了人民币汇率波动的GARCH族模型,实证检验了汇率制度改革以来人民币汇率波动的特征。结果显示,2005年7月21日至今,人民币的汇率收益具有显著的左厚尾特征;汇率的波动并不服从正态分布,具有集聚性;并且人民币的波动具有记忆性,随时间变化不会衰减;通过TGARCH模型的实证结果显示,人民币的汇率波动存在一定的杠杆效应,人民币汇率还不具备浮动汇率的特征。根据分析,本文认为杠杆效应的存在源自于汇率升值的单向预期,给出以下建议：通过有节奏的汇率市场化改革,以及改善国际收支双顺差,减少对升值的单向预期;央行对汇率的波动适当控制;培育人民币汇率衍生市场,增加进出口贸易企业规避汇率风险的金融产品;增加对附加值高的出口企业非汇率贸易政策支持。     

Conditional correlations in the returns on oil companies stock prices and their determinants

The identification of the forces that drive stock returns and the dynamics of their associated volatilities is a major concern in empirical economics and finance. This analysis is extremely important for determining optimal hedging strategies. This paper investigates the stock prices’ returns and their financial risk factors for several integrated oil companies, namely Bp (BP), Chevron-Texaco (CVX), Eni (ENI), Exxon-Mobil (XOM), Royal Dutch (RD) and Total-Fina Elf (TFE). We measure the actual co-risk in stock returns and their determinants “within” and “between” the different oil companies, using multivariate cointegration techniques in modelling the conditional mean, as well as multivariate GARCH models for the conditional variances. The distinguishing features of this paper are: (i) focus on the determinants of the market value of each company using the cointegrated VAR/VECM methodology; (ii) specification of the conditional variances of VECM residuals with the Constant Conditional Correlation (CCC) multivariate GARCH model of Bollerslev [(1990) Review of Economics and Statistics 72:498–505] and the Dynamic Conditional Correlation (DCC) multivariate GARCH model of Engle [(2002) Journal of Business and Economic Statistics 20:339–350]; (iii) discussion of the performance of optimal hedge ratios calculated with the DCC estimates. The “within” and “between” DCC indicate time-varying interdependence between stock return volatilities and their determinants. Moreover, DCC models are shown to produce more accurate hedging strategies.     

China: Further Evidence on the Evolution of Stock Markets in Transition Economies

We revisit the weak‐form efficiency of China's stock markets by examining its changing behaviour over the entire history of the Shanghai and Shenzhen Stock Exchanges. The Kalman Filter technique is applied to the system consisting of a time‐varying AR model and an asymmetric TGARCH equation. The estimates of predictability combined with other non‐quantifiable, evolutionary characteristics of the markets are used to infer on their efficiency. It is shown that, at their initial development stages, both the Shanghai and Shenzhen markets were inefficient. However, the past decade saw a steady convergence of the two markets towards efficiency. An abnormal leverage effect is detected for Shanghai, but no strong evidence is found that there exists the information transmission between the two markets.     

Early warning signals using AVaRs of infinitely divisible GARCH models — evidence from stock index markets

Classical time series models have failed to properly assess the risks that are associated with large adverse stock price behaviour. This article contributes to autoregressive moving average model–GARCH (ARMA–GARCH) models with standard infinitely divisible innovations and assesses the performance of these models by comparing them with other time series models that have normal innovation. We discuss the limitations of value at risk (VaR) and aim to develop early warning signal models using average value at risk (AVaRs) based on the ARMA–GARCH model with standard infinitely divisible innovations. Empirical results for the daily Dow Jones Industrial Average Index, the England Financial Times Stock Exchange 100 Index and the Japan Nikkei 225 Index reveal that estimating AVaRs for the ARMA–GARCH model with standard infinitely divisible innovations offers an improvement over prevailing models for evaluating stock market risk exposure during periods of distress in financial markets and provides a suitable early warning signal in both extreme events and highly volatile markets.     

The persistence and asymmetric volatility in the Nigerian stock bull and bear markets

This paper considers the persistence and asymmetric volatility at each market phase of the Nigerian All Share Index (ASI). The estimate of the fractional difference parameter is used as a stability measure of the degree of persistence in the level of the series and in the absolute/squared returns, which are used as proxies for the volatility. Both semi-parametric and parametric methods are applied. Forms of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models, which include fractional integration and asymmetric variants are estimated at each market phase of the stock returns. The results show that the level of persistence differs between the two market phases in both level and squared/absolute return series. Apart from general asymmetry and persistence in Nigerian stocks, each market phase still presents significant persistence and asymmetry.     

Long-Memory,Asymmetry and Fat-Tailed GARCH Models in Value-at-Risk Estimation: Empirical Evidence from the Global Real Estate Markets

In this paper, we address the question of whether long memory, asymmetry, and fat-tails in global real estate markets volatility matter when forecasting the two most popular measures of risk in financial markets, namely Value-at-risk (VaR) and Expected Shortfall (ESF), for both short and long trading positions. The computations of both VaR and ESF are conducted with three long memory GARCH-class models including the Fractionally Integrated GARCH (FIGARCH), Hyperbolic GARCH (HYGARCH), and Fractionally Integrated Asymmetric Power ARCH (FIAPARCH). These models are estimated under three alternative innovation’s distributions: normal, Student, and skewed Student. To test the efficacy of the forecast, we employ various backtesting methodologies. Our empirical findings show that considering for long memory, fat-tails, and asymmetry performs better in predicting a one-day-ahead VaR and ESF for both short and long trading positions. In particular, the forecasting ability analysis points out that the FIAPARCH model under skewed Student distribution turns out to improve substantially the VaR and ESF forecasts. These results may have several potential implications for the market participants, financial institutions, and the government.

     

Volatility spillover and multivariate volatility impulse response analysis of GFC news events

This article applies two measures to assess spillovers across markets: the Diebold and Yilmaz’s (2012) spillover index and the Hafner and Herwartz’s (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility (RV) estimates taken from the Oxford-Man RV library, for the S&P500 and the FTSE, plus 10 years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index. Both data sets capture both the global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The Volatility Impulse Responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. We explore the impact of three different shocks, the onset of the GFC, the height of the GFC, and the impact of the ESDC. Our modelling includes leverage and asymmetric effects applying a multivariate GARCH model, and further analysis using both BEKK and diagonal BEKK (DBEKK) models. We find the impact of negative shocks is larger, but shorter in duration, in this case a difference between 3 and 6 months.     

Generalized method of moments and present value tests of the consumption-capital asset pricing model under transactions costs: evidence from the UK stock market

In this paper we test for the inclusion of the bid–ask spread in the consumption CAPM, in the UK stock market over the time period of 1980–2000. Two econometric models are used: first, Fisher’s (in J Appl Econometrics 9:S71–S94, 1994) asset pricing model is estimated by GMM. We obtain plausible values of all the structural parameters and transactions costs. We subsequently test the robustness of our results by extending the VAR approach proposed by Campbell and Shiller (in Rev Financ Stud 1:195–228, 1988). This is achieved with the inclusion of the normalised bid–ask spread as an independent variable in the pricing equation. Overall, the statistical tests are unable to reject the bid–ask spread as an independent explanatory variable in the C-CAPM. In addition, in the VAR specification we find that both the normalised and the absolute bid–ask spread is a significant predictor of the dividend to price ratio. The paper’s main conclusion is that transaction costs should be included in asset pricing models, as they possess independent explanatory power.      

Asymmetry and leverage in GARCH models: a News Impact Curve perspective

Models for conditional heteroskedasticity belonging to the GARCH class are now common tools in many economics and finance applications. Among the many possible competing univariate GARCH models, one of the most interesting groups allows for the presence of the so-called asymmetry or leverage effect. In our view, asymmetry and leverage are two distinct phenomena, both inspired by the seminal work of Black in 1976. We propose definitions of leverage and asymmetry that build on the News Impact Curve, allowing to easily and coherently verify if they are both present. We show that several GARCH models are asymmetric but none is allowing for a proper leverage effect. Finally, we extend the leverage definition to a local leverage effect and show that the AGARCH model is coherent with the presence of local leverage. An empirical analysis completes the paper.