Robust ranking of multivariate GARCH models by problem dimension

Theoretical models of contagion and spillovers allow for asset-specific shocks that can be directly transmitted from one asset to another, as well as indirectly transmitted across uncorrelated assets through some intermediary mechanism. Standard multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, however, provide estimates of volatilities and correlations based only on the direct transmission of shocks across assets. As such, spillover effects via an intermediary asset or market are not considered. In this article, a multivariate GARCH model is constructed that provides estimates of volatilities and correlations based on both directly and indirectly transmitted shocks. The model is applied to exchange rate and equity returns data. The results suggest that if a spillover component is observed in the data, the spillover augmented models provide significantly different volatility estimates compared to standard multivariate GARCH models.

Volatility dynamics of the US business cycle: A multivariate asymmetric GARCH approach

GARCH models play an extremely important role in financial time series. However, the parameter estimation of the multivariate GARCH model is challenging because the parameter number is square of the dimension of the model. In this paper, the model of structural vector autoregressive moving-average (ARMA) with GARCH is discussed and an efficient multivariate impulse response estimation method is proposed. First, the causal structure of the model was identified and the independent component of error term vector was estimated by DirectLiNGAM algorithm. Then, the relationship between conditional heteroscedasticity of the independent component of error term vector and that of residual vector was constructed, and the estimation of the impulse response of conditional volatility of multivariate GARCH models was translated to the estimation of the impulse response of error term vector. The independency among the independent components was translated to the impulse response estimation of the univariate case and the causal structure was maintained. Finally, the proposed estimation method was used to estimate the volatility of stock market, which proved that the method is computational efficient.

This paper analyzes the Taiwan stock market and examines its price and volatility linkages with those of the United States. In particular, it tests the hypothesis that the short‐term volatility and price changes spill over from the developed markets, mainly the United States, to the emerging Taiwan stock market. The model and the test are built upon Engle’s ARCH (autoregressive conditional heteroskedasticity) and Engle and Kroner’s M‐GARCH (multivariate generalized ARCH) models. The paper differs from previous studies on the Taiwan stock market in three respects. First, instead of using daily closing prices, it uses close‐to‐open and open‐to‐close returns to avoid the problem of overlapping samples. It carefully models the day‐of‐the‐week effect in daily data to avoid misspecification of the model. Second, to circumvent the generated regressor problem arising from the two‐step estimation procedure, it also employs the M‐GARCH model where all parameters are estimated simultaneously. Third, the misspecification test is carried out on various kinds of asymmetric ARCH factors. A substantial volatility spillover effect is found from the US stock market to the Taiwan stock market, especially for the model using close‐to‐open returns. There is also evidence supporting a spillover effect in price changes. The findings can be explained by the recent gradual opening of the Taiwan stock market to foreign investors.

Existing multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models either impose strong restrictions on the parameters or do not guarantee a well-defined (positive-definite) covariance matrix. I discuss the main multivariate GARCH models and focus on the BEKK model for which it is shown that the covariance and correlation is not adequately specified under certain conditions. This implies that any analysis of the persistence and the asymmetry of the correlation is potentially inaccurate. I therefore propose a new Flexible Dynamic Correlation (FDC) model that parameterizes the conditional correlation directly and eliminates various shortcomings. Most importantly, the number of exogenous variables in the correlation equation can be flexibly augmented without risking an indefinite covariance matrix. Empirical results of daily and monthly returns of four international stock market indices reveal that correlations exhibit different degrees of persistence and different asymmetric reactions to shocks than variances. In addition, I find that correlations do not always increase with jointly negative shocks implying a justification for international portfolio diversification.

The commonality in idiosyncratic volatility cannot be fully explained by time-varying volatility; correlated idiosyncratic volatility shocks are an important contributing factor. We empirically document this fact for various characteristic-sorted portfolios and industry portfolios. To capture the commonality in idiosyncratic volatility, we propose a novel multivariate generalized autoregressive conditional heteroscedasticity (GARCH) model called dynamic factor correlation (DFC). The DFC model has a closed-form likelihood function that allows computationally cheap estimation, even for a large number of assets. The DFC model improves statistical fit compared with existing multivariate GARCH models such as the dynamic conditional correlation model and the dynamic equicorrelation (DECO) model, achieving the lowest root mean square error and mean absolute error in simulations. Empirical tests also corroborate simulations in demonstrating the improved statistical fit of the DFC model. Mean--variance portfolio optimization using the DFC model outperforms alternative volatility models such as the historical covariance matrix and the DECO model. Out-of-sample mean--variance-efficient portfolios using the DFC model have the lowest volatility and the highest Sharpe ratios, thereby improving the investor's opportunity set. Under parametric restrictions, the DFC model reduces to the constant conditional correlation model or the DECO model.

Forecasting price of financial market crash via a new nonlinear potential GARCH model

Previous research indicates that the price‐output correlation is time varying. This paper therefore estimates a vector autoregression (VAR) model with a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) error process to obtain quarterly estimates of the price‐output correlation for the United States for the period 1876:IV‐1999:IV. The estimated correlation is usually positive before 1945 and zero during 1945‐1963. Negative correlations become important only after 1963 but do not become obviously more important than zero correlations. Prior to 1945, the estimated correlation typically is positive during both recessions and expansions. After 1945, the estimated correlation remains largely positive during recessions but becomes mainly negative during expansions, suggesting that changes in the sign of the price‐output correlation are the result primarily of changes in its sign during expansions.

In this article, we provide empirical evidence of the recent financial crisis over 2007–2009 using discrete time multivariate GARCH (MGARCH) models and continuous time modelling approaches. Using daily data for 14 countries, we investigate the return and volatility spillovers among the US and other international markets. The MGARCH results reveal positive return spillovers from the US to a number of markets, and volatility transmission is verified. The US market is prone to return and volatility transmission from a limited number of markets. The continuous time analysis finds evidence of feedback effects in some cases. Evidence shows that spillover effects intensified during the financial crisis.

A structural GARCH model: An application on South African data

ABSTRACT: Conventional knowledge of market volatility represents that two proximate financial markets operated in the same country would display a similar pattern in their time-varying volatility. In this paper, we propose that the heterogeneity in financial policy orientation of stock markets creates significant inter-market differences in terms of the volatility of stock returns, even if they are culturally and geographically linked to each other. For the empirical investigation of our proposition, the volatility data from two major stock exchanges in the Middle East, the Abu Dhabi Securities Exchange (ADX) and the Dubai Financial Market (DFM) are used. Both the ADX and DFM stock exchanges operate in the same country, the United Arab Emirates (UAE). The ADX is based in Abu Dhabi, the administrative capital, while the DFM is based in Dubai, the commercial and business hub of the UAE. They were both established in the year 2000, and their operational headquarters are located about 150 km from each other. This paper uses a multivariate GARCH model, in particular a diagonal VECH GARCH (1, 1) model to estimate volatility measures for stock returns between ADX-listed and DFM-listed stocks. The paper finds that the stock returns are significantly less volatile in the ADX compared to those in the DFM suggesting that the volatility transmission is incomplete between these two neighboring financial markets. This difference in volatility can potentially be attributed to the relatively conservative financial policies adopted by the oil-rich emirate of Abu Dhabi compared to the more market-oriented economic policies of Dubai, the country’s financial and commercial hub. Our findings have considerable implications for portfolio managers in ascertaining risk premiums when allocating investments across the two stock exchanges. For instance, this disparity in volatility should be taken into account by investors and policymakers when designing risk management strategies because it suggests that investors in the DFM may be exposed to higher levels of risk and uncertainty compared to their counterparts in the ADX. Investors operating in the DFM may require more robust risk management strategies, such as asset diversification and hedging, compared to their ASX counterparts.

This paper investigates the dynamics of agricultural production volatility spillovers between Bangladesh, India, and Pakistan. These countries were selected because of their agricultural economic importance to the South Asian region. This study uses per capita agricultural production data for the period 1961–2012, obtained from the Food and Agriculture Organization of the United Nations (FAO) statistical database, to construct and estimate a multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model. The MGARCH model is estimated utilizing the maximum likelihood method. Volatility impulse response functions are also applied to quantify the effects of independent shocks on expected conditional volatility. The model provides good statistical fit and the empirical results indicate significant cross‐country per capita agricultural production volatility spillovers among these countries.

This paper uses the bibliometric method of knowledge mapping analysis to clearly present the knowledge base and research fronts of cross-market volatility spillovers. The results provide strong evidence that, first, the general theme of volatility spillovers can be divided into a variety of research topics, four of which are on the dynamics of volatility spillovers in world financial markets of various types based on multivariate GARCH or VAR models and construct a crucial knowledge base for this field; second, three research fronts can be identified using burst analysis, and they focus on examining spillover directions and magnitudes, testing volatility spillovers related to oil markets and international risk transmission mechanism of emerging markets; and, third, the major contributing scholars come from institutions in the United States,China and European economies. Our conclusions offer some recommendations for market practitioners in their risk management and policy-making.

This paper develops a bivariate asymmetric non-linear smooth-transition Generalized Autoregressive Conditional Heteroskedasticity (GARCH) (BANST-GARCH) model to hedge the risk in the shipping freight rate market. Our dataset consists of 1,768 daily spot and forward freight agreement (FFA) prices of two tanker routesTD3 and TD5with the latter showing an asymmetric pattern. The empirical results of hedging effectiveness strongly support the concept that the BANST-GARCH model outperforms other models in both in- sample and out-of-sample periods with the largest variance reduction. Thus, our model is able to capture the asymmetric pattern in the tanker freight market. This study contributes to the literature by providing a new overview of the interaction between tanker spot and FFA markets, discovering the asymmetric effect of shocks in the shipping market, developing an advanced econometric model to capture the asymmetrical effect, and constructing a better hedge strategy on the basis of our BANST-GARCH model.

This paper collects a total of 541 groups of the RMB exchange rate to build the model of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) for forecasting of RMB exchange rate against US dollar. The empirical results show that the GARCH models can fit the series well and the prediction effects of both the GARCH (1, 1) model and the GARCH-M model are good.