Constant Conditional Correlation Research Articles

Bayesian estimation and comparison of MGARCH and MSV models via WinBUGS

This paper shows that Bayesian estimation and comparison of multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) and multivariate stochastic volatility (MSV) models with Markov Chain Monte Carlo methods could be straightforwardly and successfully conducted in WinBUGS package. And an algorithm based on the Cholesky decomposition is proposed to set as a prior for a correlation matrix. They are illustrated by applying three types of parsimonious MGARCH and MSV specifications nested in constant conditional correlations to weekly returns of five sector indexes of Shanghai Stock Exchange over the period of 28 June 2004 to 30 June 2008. Empirical results provide evidence for the superior performance of MSV models over MGARCH models and give support to the feasibility of the algorithm we presented. In addition, the estimation results also suggest the significant negative correlation between the persistency and the variability of volatilities in MSV models.

Dynamic Relatedness Analysis of Three Stock Market Return Volatility with a Factor of U.S. stock market:Empirical Study of Hong Kong, Japan, and Singapore Countries

This paper studies the associations among and the model construction of Hong Kong, Japan, and Singapore’s stock markets. In this paper we construct a dynamic conditional correlation (DCC) and a trivariate IGARCH (1, 1) model to evaluate the associations, and find that there does not exist an asymmetrical effect among the three stock markets with a factor of U.S. stock market. The result of empirical correlation analyses also shows that Japan’s stock market returns positively affect the Hong Kong and Singapore stock market returns, and the volatility of the three stock market returns interact with one another. Furthermore, the time lags of Hong Kong stock market returns do not affect the returns of the Japanese and Singapore stock markets. The variation risk of the Japan stock market returns’ volatility affects the variation risks of Hong Kong and Singapore stock market returns. Empirical results also show that both good and bad news will actually affect the variation risks of stock market returns. Therefore, based on the viewpoint of DCC, the explanatory ability of the trivariate IGARCH(1, 1) model is better than the model of the trivariate GARCH with a constant conditional correlation. The evidence suggests that stock market investors or international fund managers must evaluate the variation risk and relationships of the stock market returns’ volatility.

Volatility Spillovers from the Chinese Stock Market to Economic Neighbours

This paper examines whether there is evidence of spillovers of volatility from the Chinese stock market to its neighbours and trading partners, including Australia, Hong Kong, Singapore, Japan and USA. China's increasing integration into the global market may have important consequences for investors in related markets. In order to capture these potential effects, we explore these issues using an Autoregressive Moving Average (ARMA) return equation. A univariate GARCH model is then adopted to test for the persistence of volatility in stock market returns, as represented by stock market indices. Finally, univariate GARCH, multivariate VARMA-GARCH, and multivariate VARMA-AGARCH models are used to test for constant conditional correlations and volatility spillover effects across these markets. Each model is used to calculate the conditional volatility between both the Shenzhen and Shanghai Chinese markets and several other markets around the Pacific Basin Area, including Australia, Hong Kong, Japan, Taiwan and Singapore, during four distinct periods, beginning 27 August 1991 and ending 17 November 2010. The empirical results show some evidence of volatility spillovers across these markets in the pre-GFC periods, but there is little evidence of spillover effects from China to related markets during the GFC. This is presumably because the GFC was initially a US phenomenon, before spreading to developed markets around the globe, so that it was not a Chinese phenomenon.

Time Varying Correlations between Stock and Bond returns: Empirical evidence from Russia

The purpose of this study is to look at the relationship between the stock and the bond market of Russia. By using multivariate conditional volatility models, such as, Bollerslev (1990) CCC model, Engle (2002) the DCC model, we first examine whether the correlations between two classes of assets are constant or time varying. Secondly, to investigate the asymmetries in conditional variances, covariances, and correlations, an asymmetric version of the DCC model proposed by Cappiello et al. (2006) is adopted. The empirical results do not support the assumption of constant conditional correlation and there was clear evidence of time varying correlations between the Russian stocks and bond market. Both asset markets exhibit positive asymmetries.

Do Equity Market Correlations Really Change Over Time? The Case of the US and Asia-Pacific Markets

Existing literature suggests that conditional correlations between equity markets vary over time, and increase over periods of financial crises. I test this hypothesis on a set of eight national equity indices from the Asia-Pacific region on one hand, and the US market on the other. Tse (2000) constant conditional correlation test suggests that three out of eight market pairs exhibit constant conditional correlations. The remaining five correlations are time varying, but can be further subdivided into those that are characterized by high persistence in the dynamics, and those which display strong mean reversion graphs. Global asset managers should take these features into account when allocating funds across the Asia-Pacific as the expected diversification gains are likely to differ across the region, and depend on the characteristics of the correlation coefficients.

금융시계열 분석을 위한 다변량-GARCH 모형에서 비대칭-CCC의 도입 및 응용

다변량-GARCH 분야에서 비대칭모형에 대한 연구는 상대적으로 미진하다 (McAleer 등, 2009). 본 논문에서는 다변량-GARCH 시계열에서 비대칭 모형과 상수 조건부 상관모형(CCC)을 도입하여 모델링하는 방법론에 대해 연구하고 있다. 다변량 비대칭 변동성 모형 적합 방법을 실용적으로 소개하고 있으며 이를 이용하여 국내 다변량 시계열 분석을 상세히 예시하였다. It has been relatively incomplete in the field of financial time series to adapt asymmetric features to multivar ate GARCH processes (McAleer et al., 2009). Retaining constant conditional correlation(CCC) structure, this article pursues to introduce asymmetric GARCH modelling in analysing multivariate volatilities in time series in a practical point of view. Multivariate Korean financial time series are analyzed in detail to compar our theory with conventional methodologies including GARCH and EGARCH.

The Impact of Inflation Uncertainty on Output Growth and Inflation in Thailand*

We explore the impact of inflation uncertainty on output growth in Thailand, an emerging market economy with moderate inflation. Inflation and output uncertainty are modeled in a bivariate constant conditional correlation generalized autoregressive conditional heteroskedastic (AR(p)-cccGARCH(1,1)) specification. We include the exchange rate in the mean equations, and use the headline and core inflation rates and industrial production to generate inflation and output uncertainty series. These series are then used in Granger causality tests to make inferences about the effect of monetary policy-induced inflation uncertainty. Causality tests show a positive relation from inflation to inflation uncertainty. Additionally, increased inflation uncertainty decreases output. These results are consistent with real costs associated with moderate inflation. Finally, we find no evidence that monetary policy reduced these costs.

Interaction between Stock and Foreign Exchange Markets Under the Floating Regime: Evidence from Thailand

This paper explores the nature of the linkage between foreign exchange market and the Thai stock market using monthly data of exchange rate and stock prices during July 1997 to June 2010. The results from cointegration test in a bivariate framework show no long-run relationship between stock prices and nominal effective exchange rate. The noncausality test is thus employed to investigate the existence and direction of causality. It is found that there exists positive bidirectional causality between nominal effective exchange rate and stock prices. This evidence supports the flow-oriented theory, which indicates a positive linkage between stock prices and exchange rate. In addition, the results from a bivariate constant conditional correlation autoregressive conditional heteroskedastic model and the standard Granger causality test in multivariate framework indicate the existence of bidirectional causality between stock return and exchange rate return. Additionally, exchange rate return volatility does not cause stock return to decrease.

On the forecasting accuracy of multivariate GARCH models

SUMMARYThis paper addresses the question of the selection of multivariate generalized autoregressive conditional heteroskedastic (GARCH) models in terms of variance matrix forecasting accuracy, with a particular focus on relatively large‐scale problems. We consider 10 assets from the New York Stock Exchange and compare 125 models based 1‐, 5‐ and 20‐day‐ahead conditional variance forecasts over a period of 10 years using the model confidence set (MCS) and the superior predictive ability (SPA) tests. Model performance is evaluated using four statistical loss functions which account for different types and degrees of asymmetry with respect to over‐/under‐predictions. When considering the full sample, MCS results are strongly driven by short periods of high market instability during which multivariate GARCH models appear to be inaccurate. Over relatively unstable periods, i.e. the dot‐com bubble, the set of superior models is composed of sophisticated specifications such as orthogonal and dynamic conditional correlation (DCC), both with leverage effect in the conditional variances. However, unlike the DCC models, our results show that the orthogonal specifications tend to underestimate the conditional variance. Over calm periods, a simple assumption like constant conditional correlation and symmetry in the conditional variances cannot be rejected. Finally, during the 2007–2008 financial crisis, accounting for non‐stationarity in the conditional variance process generates superior forecasts. The SPA test suggests that, independently from the period, the best models do not provide significantly better forecasts than the DCC model of Engle (2002,Journal of Business and Economic Statistics20: 339–350) with leverage in the conditional variances of the returns. Copyright © 2011 John Wiley & Sons, Ltd.

Correlations and volatility spillovers between oil prices and the stock prices of clean energy and technology companies

In this paper, multivariate GARCH models are used to model conditional correlations and to analyze the volatility spillovers between oil prices and the stock prices of clean energy companies and technology companies. Four different multivariate GARCH models (BEKK, diagonal, constant conditional correlation, and dynamic conditional correlation) are compared and contrasted. The dynamic conditional correlation model is found to fit the data the best and generates results showing that the stock prices of clean energy companies correlate more highly with technology stock prices than with oil prices. On average, a $1 long position in clean energy companies can be hedged for 20 cents with a short position in the crude oil futures market.

Correlations Dynamics between Stock and Bond Returns: Evidence from India

This study looks at the relationship between stocks and bond market of India from December 2003 to March 2010. It examines whether the correlations between the two classes of assets are time-varying by using multivariate conditional volatility models. We start our investigation by Bollerslev (1990) Constant conditional correlation model to test whether varying correlations are statistically significant. Then we use a DCC-GARCH (1, 1) model proposed by Engle (2002) to analyze the dynamics of conditional correlations between the two assets. Our empirical results do not support the assumption of constant conditional correlation. There is clear evidence of time varying correlations between Indian stocks and bond market.

Modelling conditional correlations in the volatility of Asian rubber spot and futures returns

Asia is presently the most important market for the production and consumption of natural rubber. World prices of rubber are subject to not only to changes in demand, but also speculation regarding future markets. Japan and Singapore are the major future markets for rubber, while Thailand is one of the world's largest producers of rubber. As rubber prices are influenced by external markets, it is important to analyse the relationship between the relevant markets in Thailand, Japan and Singapore. The analysis is conducted using several alternative multivariate GARCH models. The empirical results indicate that the constant conditional correlations arising from the CCC model lie in the low to medium range. The results from the VARMA-GARCH model and the VARMA-AGARCH model suggest the presence of volatility spillovers and asymmetric effects of positive and negative return shocks on conditional volatility. Finally, the DCC model suggests that the conditional correlations can vary dramatically over time. In general, the dynamic conditional correlations in rubber spot and futures returns shocks can be independent or interdependent.

Analyzing and forecasting volatility spillovers, asymmetries and hedging in major oil markets

Crude oil price volatility has been analyzed extensively for organized spot, forward and futures markets for well over a decade, and is crucial for forecasting volatility and Value-at-Risk (VaR). There are four major benchmarks in the international oil market, namely West Texas Intermediate (USA), Brent (North Sea), Dubai/Oman (Middle East), and Tapis (Asia-Pacific), which are likely to be highly correlated. This paper analyses the volatility spillover and asymmetric effects across and within the four markets, using three multivariate GARCH models, namely the constant conditional correlation (CCC), vector ARMA–GARCH (VARMA–GARCH) and vector ARMA–asymmetric GARCH (VARMA–AGARCH) models. A rolling window approach is used to forecast the 1-day ahead conditional correlations. The paper presents evidence of volatility spillovers and asymmetric effects on the conditional variances for most pairs of series. In addition, the forecast conditional correlations between pairs of crude oil returns have both positive and negative trends. Moreover, the optimal hedge ratios and optimal portfolio weights of crude oil across different assets and market portfolios are evaluated in order to provide important policy implications for risk management in crude oil markets.

Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH speciflcation of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We flnd this multivariate speciflcation to be generally applicable once power, leverage and long-memory efiects are taken into consideration. In addition, we flnd that both the optimal fractional difierencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.

Modeling conditional correlations for risk diversification in crude oil markets

This paper estimates univariate and multivariate conditional volatility and conditional correlation models of spot, forward and futures returns from three major benchmarks of international crude oil markets, namely Brent, WTI and Dubai, to aid in risk diversification. Conditional correlations are estimated using the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), VARMA-AGARCH model of McAleer et al. (2009), and DCC model of Engle (2002). The paper also presents the ARCH and GARCH effects for returns and shows the presence of significant interdependences in the conditional volatilities across returns for each market. The estimates of volatility spillovers and asymmetric effects for negative and positive shocks on conditional variance suggest that VARMA-GARCH is superior to the VARMA-AGARCH model. In addition, the DCC model gives statistically significant estimates for the returns in each market, which shows that constant conditional correlations do not hold in practice.

Modelling Conditional Correlations in the Volatility of Asian Rubber Spot and Futures Returns

Asia is presently the most important market for the production and consumption of natural rubber. World prices of rubber are not only subject to changes in demand, but also to speculation regarding future markets. Japan and Singapore are the major futures markets for rubber, while Thailand is one of the world’s largest producers of rubber. As rubber prices are influenced by external markets, it is important to analyse the relationship between the relevant markets in Thailand, Japan and Singapore. The analysis is conducted using several alternative multivariate GARCH models. The empirical results indicate that the constant conditional correlations arising from the CCC model of Bollerslev (1990) lie in the low to medium range. The results from the VARMA-GARCH model of Ling and McAleer (2003) and the VARMA-AGARCH model of McAleer et al. (2009) suggest the presence of volatility spillovers and asymmetric effects of positive and negative return shocks on conditional volatility. Finally, the DCC model of Engle (2002) suggests that the conditional correlations can vary dramatically over time. In general, the dynamic conditional correlations in rubber spot and futures returns shocks can be independent or interdependent.

Volatility and Volatility Spillovers in Crude Oil and Precious Metals Markets

Crude oil and precious metals, silver and especially gold, prices have been more volatile in the recent years. Investors and speculators such as investment banks, hedge funds, mutual funds, etc. pay close attention to the price and volatility of these commodities. The daily returns of Brent, gold and silver from 8 April 1999 to 7 April 2009 are employed to model the volatility and volatility spillovers across markets. The univariate conditional volatility models suggest that there is time-varying volatility in all assets. Moreover, asymmetry is observed in the Brent and gold markets. For multivariate conditional volatility models, the previous gold and silver volatility have no spillovers effects to the Brent market. The previous volatility in Brent and silver are spillovers to the gold volatility, but only previous gold volatility spillovers to silver volatility. Therefore, silver and gold precious metals investors have to be aware of other precious metal market volatility. Particularly, gold investors should consider the previous Brent market volatility. Asymmetric effects exist in Brent and gold markets. Therefore, we can state that asymmetric models are clearly superior to symmetric models for the Brent and gold markets. However, rolling windows suggest that the assumption of constant conditional correlations is too restrictive.

NEGATIVE VOLATILITY SPILLOVERS IN THE UNRESTRICTED ECCC-GARCH MODEL

This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model that allows for volatility feedback of either the positive or negative sign. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the parameters of the model are nonnegative, which is a sufficient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one, we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories.

FATOS ESTILIZADOS E CORRELAÇÃO NO SETOR BANCÁRIO BRASILEIRO

Este artigo usa vários modelos univariados para determinar os
 fatos estilizados em finanças para quatro séries de ações de bancos brasileiros entre 02/08/1994 a 02/10/2000, três privados e um público. Na maior parte das séries, não há evidência de distribuição normal, há a presença de assimetria, aglomeração de volatilidade e alta persistência. Os resultados mostram que os retornos médios do banco estatal são menores do que os verificados para os três bancos privados. Através do uso do modelo de correlação condicional constante de Bollerslev (1990), verificou-se um crescimento na correlação entre as volatilidades das instituições financeiras após a implementação do programa de privatização dos bancos estatais, com destaque para o aumento da correlação entre o banco estatal e os privados.

Co‐movements between US and UK stock prices: the role of time‐varying conditional correlations

AbstractWe provide evidence on the nature of co‐movement in monthly US and UK stock returns by investigating time‐varying correlations in returns since 1980. There is a marked increase in correlations between these markets around 2000, which we attribute to globalization and model with a time‐varying smooth transition conditional correlation (STCC) GARCH specification. A double transition correlation model with time and US stock price volatility indicates that correlations not only increase over time but also during periods of high volatility. The STCC models perform well in comparison with constant and dynamic conditional correlation models in terms of both statistical and economic criteria, but we demonstrate that an investor will gain little from portfolio diversification across these two important markets. Copyright © 2009 John Wiley & Sons, Ltd.