Multivariate GARCH Research Articles

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.

Debt to the Penny and US Dollar Index: a lead-lag relationship of the US economy under impacts of the Covid-19 outbreak

PurposeThis study investigates the interactions between the US daily public debt and currency power under impacts of the Covid-19 crisis.Design/methodology/approachThe authors employ the multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) modeling to explore the interactions between daily changes in the US Debt to the Penny and the US Dollar Index. The data sets are from April 01, 1993, to May 27, 2022, in which noticeable points include the Covid-19 outbreak (January 01, 2020) and the US vaccination campaign commencement (December 14, 2020).FindingsThe authors find that the daily change in public debt positively affects the USD index return, and the past performance of currency power significantly mitigates the Debt to the Penny. Due to the Covid-19 outbreak, the impact of public debt on currency power becomes negative. This effect remains unchanged after the pandemic. These findings indicate that policy-makers could feasibly obtain both the budget stability and currency power objectives in pursuit of either public debt sustainability or power of currency. However, such policies should be considered that public debt could be a negative influencer during crisis periods.Originality/valueThe authors propose a pioneering approach to explore the relationship between leading and lagging indicators of an economy as characterized by their daily data sets. In accordance, empirical findings of this study inspire future research in relation to public debt and its connections with several economic indicators.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-08-2022-0581

Dynamic Conditional Correlation and Volatility Spillover between Conventional and Islamic Stock Markets: Evidence from Developed and Emerging Countries

This study aims to investigate the dynamic conditional correlation and volatility spillover between the conventional and Islamic stock markets in developed and emerging countries in order to develop better portfolio and asset allocation strategies. We used both multivariate GARCH (MGARCH) and multi-scales-based maximal overlap discrete wavelet transform (MODWT) approaches to investigate dynamic conditional correlation and volatility spillover between conventional and Islamic stock markets in developed and emerging countries. The results show that conventional and Islamic markets move together in the long run for a specific time horizon and present time-varying volatility and dynamic conditional correlation, while volatility movement changes due to financial catastrophes and market conditions. Further, the findings point out that Chinese conventional and Islamic stock indexes showed higher volatility, whereas Malaysian conventional and Islamic stock indexes showed comparatively lower volatility during the global financial crisis. This study provides fresh insights and practical implications for risk management, asset allocation, and portfolio diversification strategies that evaluate stock market reactions to the crisis in the international avenues of finance literature.

Risk Spillovers between Bitcoin and ASEAN+6 Stock Markets before and after COVID-19 Outbreak: A Comparative Analysis with Gold

This paper applies the multivariate GARCH models to investigate the role of Bitcoin as a hedge and safe haven for ASEAN+6 stock markets compared to gold. We used daily data for the dates 2 January 2017–20 January 2023, covering the recent COVID-19 pandemic. The empirical findings provide compelling evidence of cross-market shock and volatility transmission between stock returns and Bitcoin returns in both directions. Therefore, the dynamics of Bitcoin returns significantly influence the volatility of stock returns, and the relationship also holds in reverse. All diagonal element estimations are statistically significant for both periods, as shown by the findings of the return and volatility spillovers between the returns of gold and the ASEAN+6 stock market. For most ASEAN+6 equity markets evaluated, Bitcoin and gold are not safe havens, and their inclusion increases the portfolio downside risk.

Building Multivariate Time-Varying Smooth Transition Correlation GARCH Models, with an Application to the Four Largest Australian Banks

This paper proposes a methodology for building Multivariate Time-Varying STCC–GARCH models. The novel contributions in this area are the specification tests related to the correlation component, the extension of the general model to allow for additional correlation regimes, and a detailed exposition of the systematic, improved modelling cycle required for such nonlinear models. There is an R-package that includes the steps in the modelling cycle. Simulations demonstrate the robustness of the recommended model building approach. The modelling cycle is illustrated using daily return series for Australia’s four largest banks.

The Risk Premium on Mediterranean Emerging Stock Markets

In this paper, we test a conditional version of the international asset pricing model, using the multivariate GARCH process of De Santis and Gerard (1998). The model is estimated, over the period January 1997-March 2007, for five markets: the global, USA, Egyptian, Turkish and Israeli markets. We analyze a version of the ICAPM with a constant market risk price as well as the exchange rate risk price, while the conditional covariances vary over time. The results show that risk premium vary significantly across markets and over time, for all stock markets the contribution of currency premium to the total risk premium is economically significant. This study confirms that currency risk is a significant factor in the international valuation of financial assets.

Hedging strategies among financial markets: the case of green and brown assets.

Recognizing the growing importance of the green energy market-renewable energy stocks and bonds-and its classification as a viable financial asset, this paper examines hedging strategies with brown market instruments-gold, oil, bond and the composite S&P500-on the green energy markets. That is, we examine whether, and to what extent brown assets can provide a hedge for green assets, using variants of the multivariate GARCH framework (DCC, ADCC and GO-GARCH). Our dataset spans the period 01/12/2008 to 30/09/2021. To account for the influence of the COVID-19 pandemic, we split the dataset into two-pre-covid (1/12/2008-10/03/2020) and covid-era (11/03/202-30/09/2021). Two key findings emanate from our results: first, conventional bonds and stocks provide the most consistent hedge for investment in the green markets. Second, the results are sensitive to the state of the market-hedging effectiveness declined during the covid period in the green stock market. Among other things, it is recommended that investors include instruments of the green market in portfolio allocation.

Assessing the accuracy of exponentially weighted moving average models for Value-at-Risk and Expected Shortfall of crypto portfolios

A plethora of academic papers on generalized autoregressive conditional heteroscedasticity (GARCH) models for bitcoin and other cryptocurrencies have been published in academic journals. Yet few, if indeed any, of these are employed by practitioners. Previous academic studies produce results that are fragmented, confusing and conflicting, so there is no commercial incentive to drive an expensive implementation of complex multivariate GARCH models, which anyway would commonly require more data for calibration than are available in the history of most cryptocurrencies, at least at the daily frequency. Consequently, this paper assesses the forecasting accuracy of simple parametric RiskMetrics type volatility and covariance models, with a focus on ad hoc parameter choice instead of a data-intensive calibration procedure. We provide extensive backtests of hourly and daily Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts that are regarded as best practice in the industry and commonly used for regulatory approval. Our results demonstrate that much simpler models in the exponentially weighted moving average (EWMA) class are just as accurate as GARCH models for VaR and ES forecasting, provided they capture an asymmetric volatility response and a heavy-tailed returns distribution. Moreover, on ranking each model's variance and covariance forecasts using average scores generated from proper univariate and multivariate scoring rules, there is no evidence of superior performance of variance and covariance forecasts generated by GARCH models, using either daily or hourly data.

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.

FAANG Stocks, Gold, and Islamic Equity: Implications for Portfolio Management during COVID-19

During the COVID-19 pandemic, technology stocks, such as FAANG stocks (Facebook, Amazon, Apple, Netflix, and Google), attracted the attention of global investors due to the vast use of technology in daily business. However, technology stocks are generally considered risky stocks; hence, efficient risk management is required to construct an optimal portfolio. In this study, we investigate the volatility spillovers and dynamic conditional correlations among the daily returns of FAANG company stocks, gold, and sharia-compliant equity to construct the optimal portfolio weights and hedge ratios during the COVID-19 pandemic period by utilizing a multivariate GARCH framework. The dynamic conditional correlations reveal that both gold and sharia-compliant equities exhibit lower correlations with FAANG stocks during the COVID-19 pandemic, implying opportunities for portfolio diversification. The findings indicate that gold and shariah-compliant equity are good candidates to hedge FAANG stocks. These findings are highly relevant for international investors, asset managers, hedgers, and portfolio managers.

Price volatility transmission in the value chain of fresh anchovies in Spain

This study examines the price volatility transmission of fresh anchovies (Engraulis encrasicolus) among different markets along the value chain in Spain. For this purpose, the prices in the first-hand sale, wholesale, and retail markets are considered. A vector autoregressive (VAR) model and an asymmetric multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) model are used to analyse the relationship of price volatility among the markets in the value chain. The results indicate that the retail market has the lowest volatility. Therefore, volatility in the first-hand sale and wholesale markets is only minimally transmitted to consumers. Finally, asymmetric effects are observed in the price volatility transmission along the fresh anchovy value chain.

A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization With MGARCH and Small Transaction Costs

We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter ϵ > 0 that controls the magnitude of transaction costs. When ϵ is small, we can implement an NN algorithm based on the expansion of the solution in powers of ϵ. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.

The Effect of COVID-19 on Cryptocurrencies and the Stock Market Volatility: A Two-Stage DCC-EGARCH Model Analysis

This research examines the correlations between the return volatility of cryptocurrencies, global stock market indices, and the spillover effects of the COVID-19 pandemic. For this purpose, we employed a two-stage multivariate volatility exponential GARCH (EGARCH) model with an integrated dynamic conditional correlation (DCC) approach to measure the impact on the financial portfolio returns from 2019 to 2020. Moreover, we used value-at-risk (VaR) and value-at-risk measurements based on the Cornish–Fisher expansion (CFVaR). The empirical results show significant long- and short-term spillover effects. The two-stage multivariate EGARCH model’s results show that the conditional volatilities of both asset portfolios surge more after positive news and respond well to previous shocks. As a result, financial assets have low unconditional volatility and the lowest risk when there are no external interruptions. Despite the financial assets’ sensitivity to shocks, they exhibit some resistance to fluctuations in market confidence. The VaR performance comparison results with the assets portfolios differ. During the COVID-19 outbreak, the Dow (DJI) index reports VaR’s highest loss, followed by the S&P500. Conversely, the CFVaR reports negative risk results for the entire cryptocurrency portfolio during the pandemic, except for the Ethereum (ETH).

The Corelation of Pandemic and Indonesia Presidency of G20 in The Capital Market G20 Member Countries

The correlation between the capital market of G20 member countries is important to analyze.Depending on a country’s economy, capital market integration may have different effects. A more intensebilateral relationship (trade intensity) can significantly affect the movement of capital market sharesbetween countries. The current research used the Multivariate GARCH Model/DCC-GARCH method. Thecondition of capital market integration before the Indonesian G20 Presidency showed that Indonesia(JKSE) had the strongest integration with Australia (ASX) (0.563814) and South Korea (KOSPI) (0.542470).After the G20 presidency, Indonesia (JKSE) had the strongest capital market integration with India (NSE)(0.507229) and the USA (NYSE). It was also found that China (SSE) had an integration with South Korea(KOSPI), while Germany (DAX) and Australia (ASX) had an integration with the UK (FTSE100). Theconclusion is that the higher autocorrelation, the higher the effect of the volatility of stock marketmovements in the two countries involved. Furthermore, capital market integration can be influenced bygeospatial and economic relations.

Financial Market Linkages in South Asia: Evidence Using a Multivariate GARCH Model

The economic and social benefits of more openness and internationalisation are well supported by both academics and policy-makers. Many countries are also trying to become part of the world trade bloc such as the World Trade Organisation (WTO) or AFTA. Efforts are also made to strengthen the existing regional economic and trade coordination or establish new regional economic and financial integration. Unfortunately, at the time (during the 1980s and 1990s) when many emerging economies in East Asia were involved in openness, internationalisation and regional economic and financial integration, the South Asian countries wasted their resources in dealing with political crisis (such as Bangladesh), internal conflicts (such as Sri Lanka) or border issues (such as India and Pakistan). It is only recently that regimes have realised that a peaceful economic environment is essential to attract foreign investment, pursue a pro-growth policy and achieve a sustainable growth. The recent dialogue between Pakistan and India and some progress in SAARC consultation are a few steps towards these goals.

Are Sustainability Indices Infected by the Volatility of Stock Indices? Analysis before and after the COVID-19 Pandemic

Considering the growing importance of sustainable investments worldwide, we explore the volatility transmission effects between the EURO STOXX Sustainability Index and the stock market indexes of its stocks. Using daily index return data, during 2000–2022, covering the COVID-19 pandemic, Multivariate Generalized Auto-Regressive Conditional Heteroskedasticity (MGARCH) models are used to explore if volatility effects of the stock indices felt during the pandemic implied any evolution in the effects already felt between the volatilities existing in these stock indices and the effects of stock market indices’ volatility over the sustainability index. Results point to the great dependence that the sustainability index has on stock index movements. The volatility felt in stock indices during the pandemic period did not become decisive in reversing a previous correlation trajectory between the stock market and sustainability indexes. Provided that sustainability is not observed exclusively in financial and economic terms, but in a triple bottom line context (including the social and environmental sides), we should not verify a high influence of stock market indexes over the sustainability index, as the results point out. Policymakers and investors should be aware of the high influence and take measures to turn the sustainability index more independent.

Dynamic risk management in European energy portfolios: Evolution of the role of clean and carbon markets

This paper examines the potential of clean energy stocks and emission permits to reduce downside risk when combining them in a portfolio with dirty energy assets. We propose a strategy for building portfolios that are well diversified between equity energy and carbon markets that takes into account their dynamic price relationship. The asset allocation proposed is framed in a volatility-timing context, which reacts to changing market conditions, holding different weights at different times. To achieve this objective, we use multivariate GARCH models, specifically the Asymmetric Dynamic Conditional Correlations family, which allow us to obtain good estimations of the conditional covariance matrices of the daily asset returns. To determine the weights of the optimum minimum-risk portfolio, we use a method based on Engle and Colacito (2006) to compare the portfolio volatilities obtained with different models. The analysed period runs from January 19, 2010, to April 4, 2022, which, on the one hand, includes more than twelve years of the EU Emissions Trading System (EU ETS) beyond the Phase I pilot; and, on the other, considers the latest crisis episodes (Sovereign debt crisis, Brexit COVID-19, and the recent Russo–Ukrainian war). Our findings show that investing in clean energy companies is now valuable not only because of its contribution to a sustainable energy transition to renewable sources, but also due to its attractiveness from a financial point of view. This fact provides a ray of hope in terms of the climate emergency and avoiding the current geopolitical conflicts principally caused by certain countries’ energy dependence because their energy mix is still heavily overpowered by fossil fuels. The results of this research should encourage investors to decarbonise their equity portfolios, thus promoting the needed alignment of the financial system with the requirements of the energy transition.

Dependence and spillover among oil market, China's stock market and exchange rate: new evidence from the Vine-Copula-CoVaR and VAR-BEKK-GARCH frameworks

We first employ the method of multivariate GARCH models and Vine-Copula-CoVaR to analyse relationships between dependence, systematic risk spillover, and volatility spillover between the USD/CNY exchange rate and the returns on WTI crude oil futures and the Chinese stock market since China's 2005 foreign exchange reform. We utilise daily data from 2005 to 2020. We find a more complex dependence of the USD/CNY exchange rate on stock markets and WTI crude oil prices. All have negative risk spillovers among paired markets, with WTI having the most substantial risk spillover. However, the strength of the systematic risk spillover varies across markets. Based on the results of the VAR(1)-BEKK-GARCH (1,1) and Wald tests confirm that there is a substantial mean spillover from the Chinese stock market and the USD/CNY exchange rate to the WTI crude oil price, whereas there is a more significant spillover from the WTI crude oil price to Chinese stock market volatility. The empirical findings extend the systematic understanding of the international crude oil price shocks to the dependence and transmission mechanism between the Chinese stock market and the USD/CNY exchange rate (USD/CNY). Our findings can help investors and policymakers to manage risk better and develop more sensible market rules.

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models.

Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified dynamic conditional correlation (DCC) model that accommodate external time-varying predictors for the within-person variance. The main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, 3 components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. These models allow for variance spillover effects from one time-series to another. We illustrate the pdBEKK- and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance. Overall, the pdBEKK seems to result in a more straightforward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect nonzero parameters. We provide an R-package bmgarch that facilitates the estimation of these types of models. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Bayesian inference of multivariate-GARCH-BEKK models

The main aim of this paper is to present a Bayesian analysis of Multivariate GARCH(l, m) (M-GARCH) models including estimation of the coefficient parameters as well as the model order, by combining a set of existing MCMC algorithms in the literature. The proposed algorithm focuses on the BEKK formulation of the multivariate GARCH model. The estimation procedure will be designed as a custom MCMC with embedded Reversible Jump MCMC (RJMCMC) and Delayed Rejection Metropolis-Hastings (DRMH) steps implemented using the statistical software R. The RJMCMC steps allow three variants of BEKK models (constant, diagonal and full) to be indexed and this index included as a parameter to be estimated. The proposed MCMC algorithms are validated using extensive simulation experiments followed by a case study using bivariate data derived from the daily share prices for BHP Group Limited, Rio Tinto Group, and Fortescue Metals Group Limited on the ASX over from September 2013 to December 2021.