Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension of the parameter space is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian for a variety of multivariate GARCH models including the Vec and BEKK specifications as well as the recent dynamic conditional correlation model. By means of a Monte Carlo investigation of the BEKK–GARCH model we illustrate that employing analytical derivatives for inference is clearly preferable to numerical methods.     

BAYESIAN INFERENCE METHODS FOR UNIVARIATE AND MULTIVARIATE GARCH MODELS: A SURVEY

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non‐parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non‐parametric approach.     

我国沪、深股市的波动性研究——基于GARCH族模型

金融市场的波动性不仅是投资者关注的焦点之一,而且也是被研究的热点之一。中国股市还非常年轻,股票市场的价格常常表现出大幅波动的特征。本研究以上证综合指数和深圳成分指数为研究对象,分别运用GARCH模型、TARCH模型和EGARCH模型同时拟合,并对比分析了中国股市日收益率波动的动态特征;结果显示,EGACH模型能更有效拟合股市的波动性。     

Macroeconomic forecasting using penalized regression methods

We study the suitability of applying lasso-type penalized regression techniques to macroe-conomic forecasting with high-dimensional datasets. We consider the performances of lasso-type methods when the true DGP is a factor model, contradicting the sparsity assumptionthat underlies penalized regression methods. We also investigate how the methods handle unit roots and cointegration in the data. In an extensive simulation study we find that penalized regression methods are more robust to mis-specification than factor models, even if the underlying DGP possesses a factor structure. Furthermore, the penalized regression methods can be demonstrated to deliver forecast improvements over traditional approaches when applied to non-stationary data that contain cointegrated variables, despite a deterioration in their selective capabilities. Finally, we also consider an empirical applicationto a large macroeconomic U.S. dataset and demonstrate the competitive performance of penalized regression methods.     

Multivariate semi-nonparametric distributions with dynamic conditional correlations

This paper generalizes the Dynamic Conditional Correlation (DCC) model of Engle (2002), incorporating a flexible non-Gaussian distribution based on Gram-Charlier expansions. The resulting semi-nonparametric-DCC (SNP-DCC) model allows estimation in two stages and deals with the negativity problem which is inherent in truncated SNP densities. We test the performance of a SNP-DCC model with respect to the (Gaussian)-DCC through an empirical application of density forecasting for portfolio returns. Our results show that the proposed multivariate model provides a better in-sample fit and forecast of the portfolio returns distribution, and thus is useful for financial risk forecasting and evaluation.     

基于波动率的货币与产出关系检验——来自分位数回归模型的新证据

本文使用1991年1月到2012年3月的样本数据对货币波动率和实际产出波动率之间的关系进行了检验。首先,应用GARCH模型度量货币波动率和产出波动率,进而对二者进行了Granger因果关系检验,发现我国货币供给增长率及其波动率对实际产出增长率及其波动率具有解释和预测能力。其次,使用分位数回归模型研究产出波动率在较小(低分位数)和较大(高分位数)时对货币供给量M0和M1波动率的不同反应程度。最后,提出了稳定产出增长,防止产出剧烈波动的货币政策建议。     

Multimodality in GARCH regression models

It is shown empirically that mixed autoregressive moving average regression models with generalized autoregressive conditional heteroskedasticity (Reg-ARMA-GARCH models) can have multimodality in the likelihood that is caused by a dummy variable in the conditional mean. Maximum likelihood estimates at the local and global modes are investigated and turn out to be qualitatively different, leading to different model-based forecast intervals. In the simpler GARCH(p,q) regression model, we derive analytical conditions for bimodality of the corresponding likelihood. In that case, the likelihood is symmetrical around a local minimum. We propose a solution to avoid this bimodality.     

The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.     

Forecasting sales response for multiple time horizons and temporally aggregated data: A comparison of constant and stochastic coefficient models

Past research on time-varying sales-response models emphasized the application of different estimation techniques in examining variation in advertising effectiveness over time. This study focuses on comparing sales forecasts using constant and stochastic coefficients sales-response models. Selected constant and stochastic coefficient models are applied to six sets of bimonthly and one set of annual advertising and sales data to assess forecasting accuracy for time horizons of various lengths. Results show improved forecasting accuracy for a first-order autoregressive stochastic coefficient model, particularly in short-run forecasting applications.     

Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

上海期货交易所的涨跌停板制度对波动性的影响

本文通过对上海期货交易所的三个品种的涨跌停板制度进行检验,检验方法为:从收益率所拟和的ARMA模型中滤出残差,进行波动率的GARCH模型回归。波动率模型中加入了哑元变量来体现涨停板对后一日波动的影响。实证结果显示,铜、铝、天然橡胶的涨跌停板本应显著地使收益率的波动率减小的作用未检验出,相反却得到涨停板使三个品种显著波动率增大的检验结果。是否需要扩大涨跌停板,提高市场效率?检验结果带给我们如何使涨跌停板制度趋于合理化的思考。