Threshold, news impact surfaces and dynamic asymmetric multivariate GARCH

DAMGARCH is a new model that extends the VARMA-GARCH model of Ling and McAleer (2003) by introducing multiple thresholds and time-dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset-specific shocks and common innovations by partitioning the multivariate density support. This paper presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasi-maximum likelihood estimators. The paper also presents an empirical example to highlight the usefulness of the new model

Ten Things you should know about DCC

The purpose of the paper is to discuss ten things potential users should know about the limits of the Dynamic Conditional Correlation (DCC) representation for estimating and forecasting time-varying conditional correlations. The reasons given for caution about the use of DCC include the following: DCC represents the dynamic conditional covariances of the standardized residuals, and hence does not yield dynamic conditional correlations; DCC is stated rather than derived; DCC has no moments; DCC does not have testable regularity conditions; DCC yields inconsistent two step estimators; DCC has no asymptotic properties; DCC is not a special case of GARCC, which has testable regularity conditions and standard asymptotic properties; DCC is not dynamic empirically as the effect of news is typically extremely small; DCC cannot be distinguished empirically from diagonal BEKK in small systems; and DCC may be a useful filter or a diagnostic check, but it is not a model

Model Selection and Testing of Conditional and Stochastic Volatility Models

This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage

Robust Ranking of Multivariate GARCH Models by Problem Dimension

During the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. Recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. We provide an empirical comparison of alternative MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC), CCC, OGARCH Exponentially Weighted Moving Average, and covariance shrinking, using historical data for 89 US equities. We contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC and covariance shrinking models. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Model Confidence Set. Third, we examine how the robust model rankings are influenced by the cross-sectional dimension of the problem

Forecasting Value-at-Risk Using Block Structure Multivariate Stochastic Volatility Models

Most multivariate variance or volatility models suffer from a common problem, the “curse of dimensionality”. For this reason, most are fitted under strong parametric restrictions that reduce the interpretation and flexibility of the models. Recently, the literature has focused on multivariate models with milder restrictions, whose purpose was to combine the need for interpretability and efficiency faced by model users with the computational problems that may emerge when the number of assets is quite large. We contribute to this strand of the literature proposing a block-type parameterization for multivariate stochastic volatility models. The empirical analysis on stock returns on US market shows that 1% and 5 % Value-at-Risk thresholds based on one-step-ahead forecasts of covariances by the new specification are satisfactory for the period includes the global financial crisis

Are the S&P 500 Index and Crude Oil, Natural Gas and Ethanol Futures Related for Intra-Day Data?

The energy sector is one of the most important in the world, so that time series fluctuations in leading energy sources have been analysed widely. As the leading energy commodities are traded on international stock exchanges, the analysis of the fluctuations in stock and financial derivatives prices and returns have also been investigated extensively in recent years. Much of the empirical analysis has concentrated on using daily, weekly or monthly data, with little research based on intra-day data. The paper analyses the relationships among the S&P 500 Index and futures prices, returns and volatility of three leading energy commodities, namely crude oil, natural gas and ethanol, using intra- day data. The detailed analysis of intra-day temporal aggregation in examining returns relationships and volatility spillovers across the equity and energy futures markets, and the effects of overnight returns, volume, realized volatility, asymmetry, and spillovers across the four financial markets, leads to interesting and useful results for decision making and hedging strategies. The empirical results relating to alternative models of mean and variance feedback and asymmetry for intra-daily returns, asymmetry and volatility spillovers, and dynamic conditional correlations and covariances, show that the relationships between the stock market and alternative energy financial derivatives, specifically futures prices and returns, can and do vary according to the trading range, whether daily or overnight effects are considered, and the temporal aggregation and time frequencies that are used