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Macroeconomic or financial data are often modelled with cointegration and GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity). Noticeable examples include those studies of price discovery in which stock prices of the same underlying asset are cointegrated and they exhibit multivariate GARCH. It was not until recently that Li, Ling, and Wong's (2001) Biometrika, 88, 1135–1152, paper formally derived the asymptotic distribution of the estimators for the error-correction model (ECM) parameters, in the presence of conditional heteroskedasticity. As far as ECM parameters are concerned, the efficiency gain may be huge even when the deflated error is symmetrically distributed. Taking into consideration the different rates of convergence, this paper first shows that the standard distribution applies to a portmanteau test, even when the conditional mean is an ECM. Assuming the usual null of no multivariate GARCH, the performance of this test in finite samples is examined through Monte Carlo experiments. We then apply the test for GARCH to the yearly or quarterly (extended) Nelson–Plosser data, embedded with some prototype multivariate models. We also apply the test to the intra-daily HSI (Hang Seng Index) and its derivatives, with the spread as the ECT (error-correction term). The empirical results throw doubt on the efficiency of the usual estimation of the ECM parameters, and more importantly, on the validity of the significance tests of an ECM.

The purpose of this paper is to examine the effects of inflation uncertainty on real economic activity using data from four industrialised countries.

The paper uses the econometric framework developed by Elder in the context of a multivariate framework in which a structural vector autoregression (VAR) is modified to accommodate multivariate GARCH‐in‐mean (MGARCH‐M) errors. It calculates the impulse response functions for the multivariate GARCH(1,1)‐in‐mean VAR in order to see whether the specification captures the fundamental dynamics.

The results show that inflation uncertainty has differential effects on output growth across these countries.

In the context of multivariate GARCH(1,1)‐in‐mean VAR, this paper uses a non‐recursive identification scheme and separate identification for the large and small economies.

The purpose of this paper is to analyze the nature of returns and volatility spillovers between exchange rates and stock price in the IBSA nations (India, Brazil, South Africa).

The study uses VAR framework and the recently proposed Spillover measure of Diebold and Yilmaz to examine the returns and volatility spillover between exchange rates and stock prices of IBSA nations. In addition, multivariate GARCH with time varying variance‐covariance BEKK model is used as a benchmark against the spillover methodology proposed by Diebold and Yilmaz.

The results of multivariate GARCH model suggests the integration between stock and foreign exchange markets and indicates the existence of bi‐directional volatility spillover between stock and foreign exchange markets in the IBSA countries. Spillover results using the Diebold Yilmaz model suggest the bi‐directional contribution between stock and foreign exchange market, in terms of both returns and volatility spillovers. Overall, results confirm the presence of returns and volatility spillovers within the IBSA nations and, in particular, the stock markets play a relatively more important role than foreign exchange markets in the first and second moment interactions and spillovers.

The market participants may consider the relationship between the exchange rate and stock index to predict the future movement of each other effectively. Multinational companies interested in exchange rate forecasting may consider the stock market as an important attribute. There is an interesting implication for portfolio managers too because of the spillover stock and foreign exchange markets. This knowledge would help to create a fund which performs well. Moreover, the paper can help regulators and policy makers in IBSA nations to understand the structure of the market in a better way and then design their policies.

The study contributes to the literature by extending the existing studies on the spillover between stock price and exchange rate by investigating the issue for three emerging economies, India, Brazil and South Africa. Unlike most studies in the literature which focus on multivariate GARCH model, this is the first study which explores the issue of returns and volatility spillover between the stock prices and the exchange rates using spillover measure of Diebold and Yilmaz and much longer and recent daily data. Moreover, multivariate GARCH with time varying variance‐covariance BEKK model is used as a benchmark against the spillover methodology proposed by Diebold and Yilmaz.

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 purpose of this paper is to investigate empirically contagion channels of the 2007 US subprime financial crisis by employing a multivariate GARCH model for four major, international equity markets, namely the USA, EMU, China and Japan.

In this study, contagion channels of the 2007 US subprime financial crisis are investigated empirically by employing a multivariate GARCH model for four major, international equity markets, namely the USA, EMU, China and Japan.

There is empirical evidence of contagion in all markets with the US market through various channels, which have not been discussed in other related studies. Specifically, the empirical results suggest that Japanese and EMU markets have been directly affected from the crisis. However, while China's equity market has been mainly unaffected by the US subprime crisis, has been affected indirectly through Japan. Moreover, the Japanese equity market exhibits positive and significant spillovers effects with China and EMU, revealing an indirect volatility transmission channel of US subprime crisis.

Further research could consider the asymmetric effects on conditional covariance through, for example, asymmetric generalized dynamic conditional correlation models. All under examination markets show evidence of contagion through different channels.

Despite the financial advices for diversification, since the increasing globalization and stock market interdependence throughout the last 15 years, through the US subprime crisis equity investors had fewer opportunities for diversification. From policy makers' perspective, they should carefully examine and uncover possible decoupling strategies to insulate these economies from contagion in future crises.

This study provides useful information to international organizations, such as World Bank and World Trade Organization (WTO) in order to protect markets from contagion during future crises.

A novel finding of this paper is the indirect channel of contagion (i.e. Japanese market) for Chinese market. This indirect channel may help explain why China's equity market performed badly in 2008 after the subprime crisis in the USA emerged.

The purpose of this paper is to evaluate selected West African currencies/US dollar exchange rates for the evidence of volatility spillover. Specifically, the paper examines West African CFA franc, Gambian dalasi and Nigerian naira exchange rates in relation to the USD, for any evidence of shock and volatility spillover.

The author employs multivariate GARCH (1,1)–BEKK model which enables the evaluation of the interaction within the volatility of two or more series because of its capability to detect volatility spillover among time series observations, as well as the persistence of volatility within each series.

The major findings of this study are as follows: there is evidence of volatility clustering in West African CFA franc, Gambian dalasi and Nigerian naira exchange rates in relation to the USD. There is evidence of bi-directional shock and volatility spillover between the Nigerian naira and West African CFA franc/USD exchange rates, and uni-directional shock spillover from the Gambian dalasi to the West African CFA franc/USD exchange rates. There is, however, no evidence of exchange rate shock and volatility spillover between Nigerian naira and Gambian dalasi.

Although considerable literature exists on the volatility of exchange rate in West Africa and comparative analysis of exchange rates volatility in few countries of West Africa, there is absence of empirical studies on exchange rate volatility spillover among countries in the region. Since containing exchange rate volatility is one of the major objectives of monetary policy, understanding the nature and direction of exchange rate volatility spillover would propel formulation exchange rate policies that would minimise exchange rate uncertainty and entrench sustainable development. In addition, the nature of exchange rate volatility spillover between West African countries would provide basis for international traders and foreign portfolio investors to develop effective strategies for hedging against exchange rate shocks that are propagated across countries by designing appropriate risk management techniques.

This study employs a multivariate GARCH model to investigate the relative sensitivities of the first and the second moment of bank stock return distribution to the short‐term and long‐term interest rates and their respective volatilities. Three portfolios are formed representing the money center banks, large banks, and small banks, respectively. Estimation and testing of hypotheses are carried out for each of the three portfolios separately. The sample includes daily data over the 1988‐2000 period. Several hypotheses are tested within the multivariate GARCH specification. These include the hypotheses of: (i) insensitivity of bank stock return to the changes in the short‐term and long‐term interest rates, (ii) insensitivity of bank stock returns to the changes in the volatilities of short‐term and long‐term interest rates, and (iii) insensitivity of bank stock return volatility to the changes in the short‐term and long‐term interest rate volatilities. The findings indicate that short‐term and long‐term interest rates and their volatilities do exert significant and differential impacts on the return generation process of the three bank portfolios. The magnitudes and the direction of the effect are model‐specific namely that they depend on whether the short‐term or the long‐term interest rate level is included in the mean return equation. These findings have implications on bank hedging strategies against the interest rate risk, regulatory decisions concerning risk‐based capital requirement, and investor’s choice of a portfolio mix.

The purpose of this paper is to quantify the extent to which the Malaysia-based equity investors can benefit from diversifying their portfolio into the conventional and Islamic Southeast Asian region and the world’s top ten largest equity indices (China, Japan, Hong Kong, India, the UK, the USA, Canada, France, Germany and Switzerland).

The multivariate GARCH-dynamic conditional correlation is deployed to estimate the time-varying linkages of the selected conventional and Islamic Asian and international stock index returns with the Malaysian stock index returns, covering approximately eight years daily starting from 29 June 2007 to 30 June 2016.

In general, in terms of volatility, the results indicate that both Asian and international Islamic stock indices are more or less volatile than its conventional counterparts. From the correlation analysis, we can see that both the conventional and Islamic MSCI indices of Japan provide more diversification benefits compared to Southeast Asian region, China, Hong Kong and India. Meanwhile, in terms of international portfolio diversification, the results tend to suggest that both the conventional and Islamic MSCI indices of the USA provide more diversification benefits compared to the UK, Canada, France, Germany and Switzerland.

The findings of this paper may have several significant implications for the Malaysia-based equity investors and fund managers who seek for the understanding of return correlations between the Malaysian stock index and the world’s largest stock market indices in order to gain higher risk-adjusted returns through portfolio diversification. With regard to policy implications, the findings on market shocks and the extent of the interdependence of the Malaysian market with cross-border markets may provide some useful insights in formulating effective macroeconomic stabilization policies in the efforts of preventing contagion effect from deteriorating the domestic economy.

The aim of this study is to measure portfolio diversification benefits of the Turkey-based equity investors into top trading partner countries. Portfolio diversification benefits are analyzed from the viewpoint of two types of investors in Turkey: conventional equities investors and Islamic equity investors.

In order to evaluate the time-varying correlations of the trading partner country's stock index returns with the Turkish stock index returns, the multivariate-generalized autoregressive conditional heteroskedasticity–dynamic conditional correlation (GARCH-DCC) is applied based on daily data covering 13 years' period between January 22, 2008 and January 22, 2021.

The results revealed that the US stock indices provide the most diversified benefit for both conventional and Islamic Turkey-based equity investors. In general, Islamic indices exhibit relatively lower correlation with trading partners than conventional indices. Turkey and Russia are recorded as the most volatile indices.

The diversification potential in trading partners for Turkey-based Islamic equity investors has not been studied yet. This study is to fill in this gap in the literature and to give fruitful insights to both conventional and Islamic investors.

The purpose of this paper is to analyze the existence of volatility spillover effect in frontier markets. This study also examines whether any linkages exist among these markets or not.

Monthly data of regional frontier markets, from 2009 to 2016, are analyzed using Multivariate GARCH (BEKK and Dynamic Conditional Correlation (DCC)) models.

The result of cointegration test shows that the sample frontier markets are not linked in long run, and Granger causality test reveals that the markets under consideration do not cause each other even in the short run. BEKK test says that the effect of the arrival of shock from the own market does not last for longer, whereas shock from other markets lasts with the stronger persistence, and according to DCC test, the volatility spillover exists for all the markets.

The results of present study suggest that the frontier markets are not cointegrated in the long run as well as in the short run, which opens the doors for long-term investments in these markets in future, which may lead to decent returns. Long-term investors may draw the benefits from including the financial assets in their portfolios from these non-integrated frontier markets; nevertheless, they have to consider and implement diversification and hedging strategies during the period of financial turmoil, so as to protect themselves against economic and financial distress.

Significant work has been done on developed, developing and emerging markets but frontier markets are not explored much so far. This paper is an attempt to see the status of frontier stock markets as potential financial markets for diversification benefits.