Diagonal BEKK Model Research Articles

Estimating Spillover Effect from International Oil Market to Stock Market: Evidence from Korean Portfolio-Level Analysis

Using a diagonal BEKK model, this paper estimates a spillover effect from the international crude oil market to the Korean stock market. Empirical results suggest that shocks and volatility in Dubai oil prices are significantly transmitted into twenty portfolios of the Korean stock market. Also, it was found that these spillover effects dramatically rose during the year 2020, when the threat of COVID-19 was the most serious. More specifically, oil-oriented portfolios, such as the power and gas firms’ portfolio and chemical firms’ portfolio, had a greater spillover effect from the international crude oil market rather than other portfolios. Further, compared to larger-capitalization firm portfolios, small-capitalization firm portfolios had a relatively greater spillover effect. Several implications and important avenues for further research are identified.

Multivariate Garch Models Comparison in Terms of the Symmetric and Asymmetric Models

Modelling the Multivariate Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model included both symmetric and asymmetric processes. The information includes monthly data for the Consumer Price Index, Crude Oil Price, Exchange Rate, and Inflation Rate from January 2005 to December 2021. For the analysis, E-view Statistical software was employed. The aforementioned four macroeconomic variables show a tendency for volatility to cluster across time. Both symmetrical and asymmetrical processes had the volatility condition. The residual recursive plot was used to analyse the structural fluctuation in the series. The plot showed continual movement in the inflation rate as well as a downward and upward movement in the consumer price index, exchange rate, and crude oil price. The Akaike Information Criterion (AIC), Hannan-Quinn Information Criterion (HQIC), and Schwarz Information Criterion were chosen as the best models based on information criteria (SIC). Symmetric and asymmetric modelling techniques were used to create the Economic Variables Multivariate GARCH (M-GARCH) models. To calculate the covariance and correlation between the four variables, M-GARCH models were utilised. The main finding of the estimation of all M-GARCH models is that the symmetric models (Diagonal BEKK and Constant Conditional Correlation, or "CCC") have the lowest values of the model information criteria compared to the asymmetric models (Diagonal BEKK and CCC), while the asymmetric models (Diagonal VECH) have the lowest values of the model information criteria compared to the symmetric models (Diagonal VECH). Based on the findings, it was discovered that while analysing the interaction between the four economic variables returns series, the Symmetric Diagonal BEKK and CCC model outperformed the Asymmetric Diagonal VECH model.

Estimating effects of nominal exchange rates and oil price shocks in the presence of structural breaks

Macroeconomic stability is an objective emerging economy desired to achieve but oil price shocks and fluctuations in nominal exchange rates tend to restrain the ability of these economies to achieve such macroeconomic balance. Regrettably, exchange rates and oil price shocks are prone to have structural breaks in defined periods. We therefore, implemented a bivariate diagonal BEKK model, Zivot-Andrews and Bai-Perron breakpoint tests to evaluate the effect of exchange rates and oil price shocks in the presence of structural breaks on macroeconomic stability in developing countries. Break dates were observed for Benin Republic and Côte d’Ivoire between 1997M01 and 1996M09, Gambia in 2003M12, Niger in 2011M04, Ghana in 2000 and 2008, and Nigeria in 2020. All break dates were attributed to various causes including COVID-19 pandemic, the United States (US) invasion of Iraq in 2003, the US recession, and the Persian Gulf crisis. The findings showed variations in oil prices and exchange rates have a hostile impact on the level of the consumer price index (CPI) after controlling for structural breaks for all countries excluding Burkina Faso. Hence, shocks conveyed significant instability in the domestic price levels of Gambia, Benin, Niger, Ghana, and Nigeria. Models of inflation should be examined after controlling for external crises and structural breaks.

Impact of COVID-19 on returns-volatility spillovers in national and regional carbon markets in China

China wants to play a leading role in international carbon reduction and has ambitious reduction plans. China is one of the largest carbon emitters globally with an increasing trade volume in both national and regional markets. Owing to carbon emissions are regarded as key policy instruments and important financial assets thus It is important to analyze volatility spillovers between national and regional markets. The Diagonal BEKK model is used to examine daily financial returns, conditional covariances, and volatility spillovers across markets before, during, and after COVID-19. The empirical results show that the magnitudes of the spillovers during COVID-19 are much larger than before and after COVID-19 which implies the impact of COVID-19 on China's economy leads to greater risk transmission across carbon markets. China's experience (from regional to national) was useful in informing the channels of risk transmission and helping understand the relevance of carbon markets for investment decisions and public policymaking in the international carbon markets. Finally, we discuss the motivations, challenges, and possible forms of cooperation between China and the Eurozone on establishing a common carbon market are discussed.

Investigating the Co-Volatility Spillover Effects between Cryptocurrencies and Currencies at Different Natures of Risk Events

This paper examines and confirms the varying volatility of the relationship between cryptocurrency and currency markets at different time periods, such as when the market encountered multiple risk events including the US–China trade war, COVID-19, and the Russian–Ukraine war. We employ the Diagonal BEKK model and find that the co-volatility spillover effects between the returns of cryptocurrencies and currencies, with the exception of Tether and the U.S. dollar index, evolved significantly. Furthermore, the co-volatility spillover effects between cryptocurrencies and EUR have the largest effects and fluctuations. Large-cap cryptocurrencies (Bitcoin and Ethereum) have greater co-volatility spillover effects between them and currencies. Regarding the ability of cryptocurrencies to act as safe-haven for currencies, we observe that Bitcoin, Ethereum, and Tether served as safe-havens during the US–China trade war, and Bitcoin was a safe-haven during COVID-19. During the 2022 Russian–Ukraine war, Bitcoin and Tether were safe-havens. Interestingly, our findings point out that Bitcoin provides a more consistent safe-haven function for currency markets. Overall, by including multiple global risk events and a comprehensive dataset, the results support our conjecture (and earlier studies) indicating that the capabilities of cryptocurrency are time-varying and related to market status and risk events with different natures.

Contagion effect of cryptocurrency on the securities market: a study of Bitcoin volatility using diagonal BEKK and DCC GARCH models.

The fundamental aim of this study is to examine the contagion effect of Bitcoin on the National Securities Exchange, Shanghai Stock Exchange, London Stock Exchange, and Dow Jones Industrial Average by analyzing the volatility spillover and correlation between these markets to understand the short-term and long-term impact of this volatility ranging from the shocks during the period March 2017–May 2021. Irrespective of ups and downs happening in the cryptocurrency market, more investors are investing their money in the cryptocurrency market. This paper will contribute to the existing literature by studying volatility spillover in the market, its contagion effect, and to identify if there is a long-term and short-term impact between the Bitcoin and stock markets facilitating the transmission of volatility spillover. We employed the Diagonal BEKK and DCC MGARCH models to investigate the integration between Bitcoin and the stock markets. From the empirical analyses, we find the overall time-varying correlation between Bitcoin and the stock markets is low, indicating that Bitcoin can be taken as an asset to hedge against the risk of these stock markets. It was also evident that these stock markets responded more to the negative shocks during 2018 and 2021 than the positive shocks in the Bitcoin market. Our study may be helpful for investment decisions, academia, and policymakers.

Inference in Misspecified GARCH‐M Models*

AbstractThe manuscript studies testing methods in systems with relationships between observed variables and conditional variances drawn from popular multivariate GARCH models. Although these methods have been extensively used to study the effects of uncertainty proxied by GARCH variables, inferential results are absent under misspecification or when using multi‐step estimators. Concentrating on test statistics for the hypothesis of no uncertainty impact, extensive Monte Carlo evidence is presented. Results show that severe size distortion and low power can occur when using two‐step procedures unless existing heteroskedasticity is modelled at every stage. In contrast, under moderate unconditional residual cross‐correlation, joint estimation of all model parameters yields test statistics with impressive relative power. In terms of misspecification, the consequences of ignoring asymmetries in the conditional variance matrix are shown to be potentially severe. Otherwise, estimation of DCC and diagonal BEKK models may be preferred relative to extended DCC and full BEKK counterparts, even under weak negative volatility spillovers. Issues are highlighted with an analysis of the relationships between production growth, inflation and their volatilities.

Modeling Mediterranean Stock Markets Volatility with Univariate and Multivariate Approaches

In our study we use the univariate and multivariate GARCH models to analyze the volatility behavior of the daily data of four Mediterranean stock markets (Morocco, Turkey, Spain, and France) spanning the period 2000-2020. We find a strong evidence of persisting of volatility in each of these markets. Results also indicate that both the univariate and the multivariate approaches capture well the ARCH and GARCH effects. We analyze the conditional covariances, and co-volatility spillovers between the Moroccan stock market and the three other Mediterranean stock markets. In order to study co-volatility spillovers, our work is built on the diagonal BEKK model especially the conditional covariances.

Asymptotic and Finite Sample Properties for Multivariate Rotated GARCH Models

This paper derives the statistical properties of a two-step approach to estimating multivariate rotated GARCH-BEKK (RBEKK) models. From the definition of RBEKK, the unconditional covariance matrix is estimated in the first step to rotate the observed variables in order to have the identity matrix for its sample covariance matrix. In the second step, the remaining parameters are estimated by maximizing the quasi-log-likelihood function. For this two-step quasi-maximum likelihood (2sQML) estimator, this paper shows consistency and asymptotic normality under weak conditions. While second-order moments are needed for the consistency of the estimated unconditional covariance matrix, the existence of the finite sixth-order moments is required for the convergence of the second-order derivatives of the quasi-log-likelihood function. This paper also shows the relationship between the asymptotic distributions of the 2sQML estimator for the RBEKK model and variance targeting quasi-maximum likelihood estimator for the VT-BEKK model. Monte Carlo experiments show that the bias of the 2sQML estimator is negligible and that the appropriateness of the diagonal specification depends on the closeness to either the diagonal BEKK or the diagonal RBEKK models. An empirical analysis of the returns of stocks listed on the Dow Jones Industrial Average indicates that the choice of the diagonal BEKK or diagonal RBEKK models changes over time, but most of the differences between the two forecasts are negligible.

Risk spillovers between cryptocurrencies and traditional currencies and gold under different global economic conditions

This paper applies a Diagonal BEKK model to investigate the risk spillovers of three major cryptocurrencies to ten leading traditional currencies and two gold prices (Spot Gold and Gold Futures). The daily data used are from 7 August 2015 to 15 June 2020. The dataset is analyzed in its entirety and is also subdivided into four distinct subsets in order to study and compare the patterns of spillover effects during economic turmoil, such as the 2018 cryptocurrency crash and the COVID-19 pandemic. The results reveal significant co-volatility spillover effects between cryptocurrency and traditional currency or gold markets, especially during the whole sample period and amid the uncertainty raised by COVID-19. The capabilities of cryptocurrency are time-varying and related to economic uncertainty or shocks. There are significant differences between normal and extreme markets with regard to the capabilities of cryptocurrency as a diversifier, a hedge or a safe haven. We find the significant co-volatility spillover effects are asymmetric in most cases especially during the COVID-19 pandemic period, which means the negative return shocks have larger impacts on co-volatility than positive return shocks of the same magnitude. Evidently, cryptocurrencies and traditional currencies or gold can be incorporated into financial portfolios for financial market participants who seek effective risk management and also for optimal dynamic hedging purposes against economic turmoil and downward movements.

Volatility spillovers for energy prices: A diagonal BEKK approach

Abstract We examine the relationship between return and volatility as well as the covolatility spillover for energy, foreign currency, and stock markets using the diagonal BEKK model. Using daily crude oil, natural gas, and the coal prices as proxies for energy prices, the S&P500 index as a proxy for the U.S. stock market, and the EUR/USD exchange rate as a proxy for the exchange rate, we find robust evidence for the volatility spillover effects among the three markets. Also, in the 16 out of 20 pairwise relationships in the five markets, there are significant negative covolatility spillover effects. In the four pairs involving coal, there are positive and significant covolatility spillover effects. We conclude that the energy markets and the stock market have stronger covolatility spillovers than others.

Volatility Modelling and Dynamic Linkages between Pakistani and Leading Foreign Stock Markets: A Multivariate GARCH Analysis

It is essential for financial institutions and academicians to understand volatility spillover and financial market returns. However, previous studies examined the effects of direct spillover only and ignored those of the newly emerging stock markets. Therefore, this study attempts to estimate the time-varying volatility of Pakistani and leading foreign stock markets. It also tries to explore the direct and indirect volatility spillover effect between Pakistani and eight leading foreign stock markets. Daily data were used from nine international equity markets (KSE 100, NIKKEI 225, HIS, S&P 500, NASDAQ 100, DOW JONES, GADXI, FTSE 350 and DFMGI) for the period between 2005 and 2016. The univariate GARCH and GJR models were employed for analysing volatility, and the multivariate GARCH Diagonal BEKK model was used to explore direct and indirect volatility spillover effects. In order to analyse the volatility spillover effect during and after the global financial crisis period, the data were categorised into two periods: between 2005 and 2009 and between 2010 and 2016. The Chow break-point test was also employed to identify structural breaks in return series due to global financial crises. Direct and indirect spillover effects were found between KSE100, S&P 500, NASDAQ 100, DOW JONES and DFMGI. Keywords: Volatility, Spillover, Equity Market, Financial Crisis and GARCH

Risk Spillovers in Returns for Chinese and International Tourists to Taiwan

Fluctuations in the numbers of visitors directly affect the rates of return on tourism business activities. This article is the first to examine the spillover effects between the rate of change in the numbers of Chinese tourist arrivals and the rate of change in the numbers of international traveler arrivals. The study used daily data from January 1, 2014, to October 31, 2016, with 1,035 observations. The diagonal BEKK model was used to analyze the co-volatility spillover effects between the rate of change in the international travelers and the rate of change in the amount of Chinese tourists visiting Taiwan. The empirical findings suggest that Taiwan should abandon its development strategy of focusing only on a single market, namely, China. Moreover, with the reduction in Chinese tour groups visiting Taiwan, and increases in individual travelers, the Taiwan Government should change its previous travel policies of mainly attracting Chinese tour group travelers and actively promote in-depth tourism among international tourists.

High frequency volatility co-movements in cryptocurrency markets

Through the application of Diagonal BEKK and Asymmetric Diagonal BEKK methodologies to intra-day data for eight cryptocurrencies, this paper investigates not only conditional volatility dynamics of major cryptocurrencies, but also their volatility co-movements. We first provide evidence that all conditional variances are significantly affected by both previous squared errors and past conditional volatility. It is also shown that both methodologies indicate that cryptocurrency investors pay the most attention to news relating to Neo and the least attention to news relating to Dash, while shocks in OmiseGo persist the least and shocks in Bitcoin persist the most, although all of the considered cryptocurrencies possess high levels of persistence of volatility over time. We also demonstrate that the conditional covariances are significantly affected by both cross-products of past error terms and past conditional covariances, suggesting strong interdependencies between cryptocurrencies. It is also demonstrated that the Asymmetric Diagonal BEKK model is a superior choice of methodology, with our results suggesting significant asymmetric effects of positive and negative shocks in the conditional volatility of the price returns of all of our investigated cryptocurrencies, while the conditional covariances capture asymmetric effects of good and bad news accordingly. Finally, it is shown that time-varying conditional correlations exist, with our selected cryptocurrencies being strongly positively correlated, further highlighting interdependencies within cryptocurrency markets.

An empirical investigation of volatility dynamics in the cryptocurrency market

By employing an asymmetric Diagonal BEKK model, this paper examines volatility dynamics of five major cryptocurrencies, namely Bitcoin, Ether, Ripple, Litecoin, and Stellar Lumen. It is shown that the conditional variances of all the five cryptocurrencies are significantly affected by both previous squared errors and past conditional volatility. Moreover, in the case of Bitcoin, Ether, Ripple, and Litecoin, asymmetric past shocks have a significant effect in the current conditional variance. Similar results are obtained for the cryptocurrencies' conditional covariances, which are significantly affected by cross products of previous error terms and past covariance terms while capturing asymmetric effects of past shocks accordingly. It is also shown that time-varying conditional correlations exist and are mostly positive. Finally, the cryptocurrencies' volatility dynamics are found to be responsive to major news, with Bitcoin and Litecoin exhibiting one structural breakpoint each in the conditional variance. The results improve our understanding of interdependencies between cryptocurrencies as well as of the events that affect their volatility dynamics and thus have important implications for both cryptocurrency users and investors.

Crude oil price shocks and hedging performance: A comparison of volatility models

From a practical perspective, it is crucial to hedge the crude oil price risk in periods of dramatic price change. In this study, we directly investigate the performance of crude oil hedge portfolios in the five periods in which the largest oil price shocks in history occurred. We use stochastic volatility (SV), GARCH, and the diagonal BEKK model to estimate the minimum variance hedge ratio of hedge portfolios. Our empirical results provide evidence that hedging strategies based on the SV model are able to outperform the GARCH and BEKK models in terms of variance reduction. Our results are also consistently valid for various hedge horizons. Interestingly, although it is important to estimate variance and covariance accurately when constructing minimum variance portfolios, we find that reducing the mean squared and mean absolute errors does not guarantee superior hedge performance.

Volatility spillovers for spot, futures, and ETF prices in agriculture and energy

The agricultural and energy industries are closely related, both biologically and financially. The paper discusses the relationship and the interactions on price and volatility, and on the covolatility spillover effects for these two industries. The interaction and covolatility spillovers, or the delayed effect of a returns shock in one asset on the subsequent volatility or covolatility in another asset, between the energy and agricultural industries is the primary emphasis of the paper. Although there has already been significant research on biofuel and biofuel-related crops, only a few published papers have been concerned with volatility spillovers. It must be emphasized that there have been numerous technical errors in the theoretical and empirical research, which need to be addressed. The paper considers futures prices as a widely-used hedging instrument, and also considers an interesting new hedging instrument, ETF, which is regarded as index futures when investors manage their portfolios. In the empirical analysis, multivariate conditional volatility diagonal BEKK models are estimated for comparing patterns of covolatility spillovers. The paper provides a new way of analyzing and describing the patterns of covolatility spillovers, which should be useful for the future empirical analysis of estimating and testing covolatility spillover effects.

Co-movements between the British pound, the euro and the Japanese yen: the Brexit impact

PurposeThe purpose of this paper is to analyze the Brexit effect – pre-Brexit and post-Brexit referendum periods – on the co-movements between the British pound (GBP), the euro (EUR) and the yen (JPY) against the US dollar (USD).Design/methodology/approachTo ascertain the asymmetric behavior of dynamic correlations, the authors use the dynamic conditional correlation (DCC) model, the asymmetric dynamic conditional correlation (A-DCC) model and the diagonal BEKK model assuming Gaussian and Student’stdistribution. Several dummy variables have been included in order to identify the main periods related to Brexit.FindingsFindings show a negative impact of the pre-Brexit referendum period on the correlation between GBP and EUR, while there is no significant effect on GBP–JPY and EUR–JPY pairs. The loss of correlation in the GBP–EUR pairing has not recovered during the post-Brexit referendum period, which could be attributed to the uncertainty about the final impact of Brexit on British and Eurozone economies.Practical implicationsThe loss of correlation in the GBP–EUR pair has important implications for individual investors, portfolio managers and traders with respect to hedging activities, international trading and investment strategies.Originality/valueThe results are the first to address how Brexit has impacted on the co-movements between exchange rates using different multivariate models that allow for correlations to change over time.

High Frequency Volatility Co-Movements in Cryptocurrency Markets

Through the application of Diagonal BEKK and Asymmetric Diagonal BEKK methodologies to intra-day data for eight cryptocurrencies, this paper investigates not only conditional volatility dynamics of major cryptocurrencies, but also their volatility co-movements. We first provide evidence that all conditional variances are significantly affected by both previous squared errors and past conditional volatility. It is also shown that both methodologies indicate that cryptocurrency investors pay the most attention to news relating to Neo and the least attention to news relating to Dash, while shocks in OmiseGo persist the least and shocks in Bitcoin persist the most, although all of the considered cryptocurrencies possess high levels of persistence of volatility over time. We also demonstrate that the conditional covariances are significantly affected by both cross-products of past error terms and past conditional covariances, suggesting strong interdependencies between cryptocurrencies. It is also demonstrated that the Asymmetric Diagonal BEKK model is a superior choice of methodology, with our results suggesting significant asymmetric effects of positive and negative shocks in the conditional volatility of the price returns of all of our investigated cryptocurrencies, while the conditional covariances capture asymmetric effects of good and bad news accordingly. Finally, it is shown that time-varying conditional correlations exist, with our selected cryptocurrencies being strongly positively correlated, further highlighting interdependencies within cryptocurrency markets.

O DESEMPENHO DO HEDGE PARA CONTRATOS FUTUROS DE BOI GORDO: UMA ANÁLISE A PARTIR DAS PRINCIPAIS PRAÇAS PRODUTORAS BRASILEIRAS

O objetivo deste estudo se deu em analisar o desempenho do hedge de boi gordo na Brasil, Bolsa, Balcão (B3) considerando as principais praças produtoras do Brasil, avaliando a razão ótima e a efetividade do hedge. Para isso, aplicou-se uma derivação do modelo clássico de razão de hedge estática, incluindo um modelo de correção de erros (VEC) e, posteriormente, com a inclusão do modelo multivariado diagonal BEKK para análise da razão e efetividade do hedge dinâmicos. Considerando o período de análise ente 2012 a 2016, nota-se, em geral, uma baixa efetividade do hedge, sobretudo nas praças mais distantes da formação dos preços. O modelo dinâmico também sugere que em nenhum momento a razão ótima do hedge supera 50%, indicando que o contrato futuro local não tem sido eficiente para atender à demanda de potenciais hedgers.