Multivariate GARCH Research Articles

Persistence and volatility spillovers of bitcoin price to gold and silver prices

The paper investigates persistence, returns and volatility spillovers from the bitcoin market to the gold and silver markets using daily datasets from January 2, 2018 to July 31, 2020 by employing the fractional persistence framework. The results show strong price persistence with bitcoin posing the highest volatility persistence, while silver poses the lowest volatility persistence. The results of multivariate GARCH modelling, using the CCC-VARMA-GARCH model and other lower variants indicate the impossibility of returns spillover between the bitcoin and gold (or silver) market, while there exist bi-directional volatility spillovers. Appropriate portfolio management and hedging strategies render towards the end of the paper require more gold and silver investments in the portfolio of bitcoin to fully have the diversification advantage and reduce risk to the minimum without reducing the expected returns of their portfolio.

Dynamic correlations and portfolio implications across stock and commodity markets before and during the COVID-19 era: A key role of gold

Novel Coronavirus (COVID-19) has affected stock markets around the globe, adding serious challenges to asset allocations and hedging strategies. This investigation analyses the dynamic correlations and portfolio implications among the S&P 500 index and various commodities (gold, WTI crude oil, Brent oil, beverages, and wheat) before and during the COVID-19 era. Using multivariate asymmetric GARCH models, the results show weak correlations during the standard period. However, the correlations intensify and become more complicated during the COVID-19 era, especially between gold and S&P 500. Similarly, bidirectional return and volatility spillovers across stock-commodity markets are more pronounced during the COVID-19 outbreak. Analysis involving the optimal portfolio weights and time-varying hedge ratios indicates that a $1long position in the S&P 500 can be hedged for 15 cents in crude oil during the standard period and for 33 cents in gold during the COVID-19 era. A portfolio of S&P 500 – beverages displays the highest VaR, while a portfolio of S&P 500 – gold displays the lowest VaR, especially during the COVID-19 era. This finding suggests that gold offers better portfolio diversification benefits and downside risk reductions, which are useful in determining strategies for portfolio investors during the COVID-19 outbreak.

A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-Varying GARCH Model

We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.

Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques

Robust fuzzy clustering of multivariate time series is addressed when the clustering purpose is grouping together series generated from similar stochastic processes. Robustness to the presence of anomalous series is attained by considering three well-known robust versions of a fuzzy C-means model based on a spectral dissimilarity measure with high discriminatory power. The dissimilarity measure compares principal component scores obtained from estimates of quantile cross-spectral densities, and the robust techniques follow the so-called metric, noise and trimmed approaches. The metric approach incorporates in the objective function a distance aimed at neutralizing the effect of the outliers, the noise approach builds an artificial cluster expected to contain the outlying series, and the trimmed approach removes the most atypical series in the dataset. As result, the proposed clustering methods take advantage of both the robust nature of these techniques and the capability of the quantile cross-spectral density to identify complex dependence structures. An extensive simulation study including multivariate linear, nonlinear and GARCH processes shows that the algorithms are substantially effective in coping with the presence of outlying series, clearly outperforming other alternative procedures. Two specific applications regarding financial and environmental series illustrate the usefulness of the presented methods.

Is Bitcoin a Safe Haven for Indian Investors? A GARCH Volatility Analysis

This paper attempts to understand the dynamic interrelationships and financial asset capabilities of Bitcoin by analysing several aspects of its volatility vis-a-vis other asset classes. This study aims to analyse the volatility dynamics of the returns of Bitcoin. An asymmetric GARCH model (EGARCH) is used to investigate whether Bitcoin may be useful in risk management and ideal for risk-averse investors in anticipation of negative shocks to the market (leverage effect). This paper also examines Bitcoin as an investment and hedge alternative to gold as well as NSE NIFTY using a multivariate DCC GARCH model. DCC GARCH models are also used to check whether correlation (co-movement) between the markets is time-varying, examine returns and volatility spillovers between markets and the effect of the outbreak of COVID-19 in India on the investigated markets. The results show that given the supply of Bitcoin is fixed, low returns realisation is equivalent to excess supply over demand wherein investors are selling off Bitcoin during bad times. The positive co-movement between Bitcoin and gold during the COVID-19 outbreak shows that investors perceived Bitcoin as a relatively safe investment. However, overall analysis shows that Bitcoin was not considered a safe hedge and an investment option by Indian investors during the study period.

Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models

Over the past years, cryptocurrencies have drawn substantial attention from the media while attracting many investors. Since then, cryptocurrency prices have experienced high fluctuations. In this paper, we forecast the high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling volatility to select the best model. We propose various generalized autoregressive conditional heteroscedasticity (GARCH) family models, including an sGARCH(1,1), GJR-GARCH(1,1), TGARCH(1,1), EGARCH(1,1), which we compare to a multivariate DCC-GARCH(1,1) model to forecast the intraday price volatility. We evaluate the results under the MSE and MAE loss functions. Statistical analyses demonstrate that the univariate GJR-GARCH model (1,1) shows a superior predictive accuracy at all horizons, followed closely by the TGARCH(1,1), which are the best models for modeling the volatility process on out-of-sample data and have more accurately indicated the asymmetric incidence of shocks in the cryptocurrency market. The study determines evidence of bidirectional shock transmission effects between the cryptocurrency pairs. Hence, the multivariate DCC-GARCH model can identify the cryptocurrency market’s cross-market volatility shocks and volatility transmissions. In addition, we introduce a comparison of the models using the improvement rate (IR) metric for comparing models. As a result, we compare the different forecasting models to the chosen benchmarking model to confirm the improvement trends for the model’s predictions.

Estimation of multivariate asymmetric power GARCH models

We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. The asymptotic properties of the quasi-maximum likelihood estimator of the parameters are established. The asymptotic results are illustrated by Monte Carlo experiments and an application to real financial data is studied.

Examining the spillover effects of volatile oil prices on Iran’s stock market using wavelet-based multivariate GARCH model

Fluctuations in the oil market can significantly influence various sectors of the economy, such as the stock markets of countries that rely heavily on oil revenues. Oil prices are one of the key influential external factors affecting the stock exchange index of oil-dependent Iran. This paper investigates the spillover effects of oil prices on Iran’s stock exchange index weekly from March 2009 to March 2020. Using a time-series wavelet decomposition approach, a series of OPEC oil prices and Iran’s total stock market index were decomposed into various time scales (4 levels) to analyze oil market spillover into the stock market using the multivariate GARCH TBEKK model. The results confirmed that volatility spillover from the oil to the stock market occurred in all the time scales (short, medium, and long term). However, the spillover in the long term is more pronounced than over the short, demonstrating that stock market volatility is strongly influenced by long-term exogenous oil price fluctuations. Hence, oil market shocks are one of the influential factors affecting stock market turbulence in Iran.

Analyzing The Covid-19 Pandemic of Volatility Spillover Influence the Collaboration of Foreign and Indian Stock Markets

One of the most crucial variables in investment selections is volatility. Unexpected information causes an investor to trade unusually in the market, which influences market volatility. Furthermore, various market sectors are affected differently by this type of trading behaviour. This research investigates the impact of COVID-19 on stock market volatility in India using a generalised autoregressive conditional model. The research was conducted using daily closing prices of stock indices include Nifty 50 and Nifty 500, from September 8, 2019, to July 9, 2021. In this article, the TGARCH model (1,1) was utilized to evaluate the volatility of NSE listed shares. The stock market's volatility has been calculated using the NSE's closing price. To reduce the skewness in the stock price data distribution, the natural logarithm of each price data is employed in the estimations. During the pre-COVID and COVID periods, the conditional volatility of the daily return series showed signs of volatility variations. Furthermore, the study aimed to compare stock price returns in pre-COVID19 and post-COVID19 scenarios to global indexes such as the NASDAQ, Nikkei 225, and FTSE. The stock market in India suffered volatility throughout the epidemic, according to the findings. Consequently, the study recommends NSE stock exchange bond indices to explore the volatility spillover influence between foreign exchange and the stock market in India. In this work, the positive definite covariance matrix is given, therefore a multivariate GARCH with BEKK model is used to estimate the covariance correlation and identify the consequences that stock market downturns can create. SPSS and Eviews software are used to analyze the data. The Augmented Dickey-Fuller (ADF) and KPSS unit root tests have been used to determine whether a time series is stationary or nonstationary. Whereas it corrects for heteroscedasticity and autocorrelation consistency in ADF test statistics, the study employed the KPSS unit root test to estimate the right result. In addition, to investigate the impact of COVID19 on stock market volatility in terms of negative and positive shocks in financial decisions, the TGARCH model captures asymmetry. The finding that the variable has a negative and statistically significant coefficient suggests that the COVID-19 outbreak lowered stock market volatility in India. In terms of historical errors, the coefficients represent the persistence of volatility for each nation. NIFTY and NASDAQ have the largest and longest-term spillover effect. According to the findings, India is the least sensitive to external shocks.

Multivariate Volatility Modeling of Nigerian Bank Share Prices

This study aims at finding the optimal Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) model among Diag-BEKK, Scalar-BEKK and CCC that captures the dynamics of returns in Nigerian bank share prices, using the data of daily share prices of two highly capitalized banks in Nigeria listed on the platform of Nigerian Stock Exchange (NSE) which span from 2nd January, 2009 to 28th December, 2019. Multivariate Normal and Multivariate student-t log-likelihood functions were simplified using the BHHH and Marquardt algorithm and the optimal solution was obtained using the information criteria. The BHHH and Marquardt algorithm was implemented in the GARCH 7 software of Laurent. Finally, the findings of this study showed that the Diag-Bekk (1,1) with Multivariate student-t distribution was the overall best model out of the six model combinations. Multivariate volatility modeling is therefore, recommended for bank share prices in Nigeria, and even in other banks from emerging economies.

On bank return and volatility spillovers: Identifying transmitters and receivers during crisis periods

This study investigates dynamic bank-return correlation and spillovers among G7 advanced markets, employing an asymmetric multivariate GARCH approach and the forecast-error variance decomposition framework of a generalized VAR model and using a time-varying parameter autoregressive model. We utilize weekly bank stock indices over a long period (2000–2020) covering the recent Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). Dynamic spillover analysis reveals evidence of contagion effects during recent episodes. It is also shown that the impact of the GFC is notably higher than that of the ESDC. Major spillover transmitters are the markets of France, Germany and the UK, with the US market being vulnerable to shocks from European markets. Useful implications arise for policy makers and investors.

Static and dynamic models for multivariate distribution forecasts: Proper scoring rule tests of factor-quantile versus multivariate GARCH models

Many static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice favours simpler, static models such as historical simulation or its variants. Most academic research focuses on dynamic models in the GARCH family. While numerous studies examine the accuracy of multivariate models for forecasting risk metrics, there is little research on accurately predicting the entire multivariate distribution. However, this is an essential element of asset pricing or portfolio optimization problems having non-analytic solutions. We approach this highly complex problem using various proper multivariate scoring rules to evaluate forecasts of eight-dimensional multivariate distributions: exchange rates, interest rates and commodity futures. This way, we test the performance of static models, namely, empirical distribution functions and a new factor-quantile model with commonly used dynamic models in the asymmetric multivariate GARCH class.

Volatility Behaviour of Bitcoin as a Digital Asset

The objective of this study is to use the South African financial markets (Johannesburg Stock Exchange or JSE and USD/ZAR) as a case study to understand the volatility spillover dynamics of Bitcoin as a digital asset. Methodologically, the study applies the exponential generalized autoregressive conditional heteroskedastic (EGARCH) model, followed by a robustness check by applying the time-varying conditional correlation multivariate GARCH (VCC-MGARCH) model. The study utilizes the data set for the period 2011 to 2019, a period before the COVID‑19 pandemic. The research outcome revealed three interesting observations. First, Bitcoin and the South African stock market are independent of each other. Second, there is a bidirectional shock transmission between Bitcoin and USD/ZAR in the mean returns only, but not variance. Lastly, results confirm the existence of a bidirectional volatility spillover in both the mean and variance between the JSE stock market and the USD/ZAR market. The study outcome should enlighten investors who may want to consider Bitcoin as a diversifier in their investment and portfolio strategies.

The Volatility Transmission Between Cryptocurrency And Global Stock Market Indices: Case Of Covid-19 Period

The uncertainty originated by the COVID-19 pandemic and the unpredictability of both real and financial market indicators have increased the volatility of global financial markets. As a result of globalization, the determination of risk and information transfer between financial markets has gained importance during the pandemic process. In this context, the spread of volatility between the cryptocurrency market and the global stock markets was analyzed by considering the pandemic process. Bitcoin, which represents 42% of the total market cap, was used to represent the cryptocurrency market in the analysis. S&P500, FTSE100, SSEC and NIKKEI indices, which are among the world's leading indices in terms of market cap, were used to represent the global stock market. Constant Conditional Correlation Multivariate GARCH model was used for the analysis of volatility transmission. Daily closing prices covering the date range from 1st December 2019 to 1st July 202 were used for the analyses. The model results were positive and significant for all predicted conditional correlation parameters. In this context, there is volatility transmission and information transfer between BTC and stock returns. The model findings are expected to be a supporting element for financial market participants to make the right decision in the optimal portfolio allocation process.

Optimal Portfolio Allocation between Global Stock Indexes and Safe Haven Assets: Gold versus the Swiss Franc (1999–2021)

This paper contributes to the literature on safe haven assets, analyzing gold and the Swiss Franc’s defensive properties inside various global stocks portfolios. The analysis relies on monthly data extending over the last two decades. Drawing on Multivariate Garch DCC models, the hedging effectiveness of bivariate Swiss Franc-hedged portfolios is found to be notably higher than that of gold-hedged portfolios. Value-at-Risk simulations, assuming equal or “optimal” portfolio weights, confirm these results inside a multivariate asset framework, while a regression approach with quantile dummies provides further support in this regard. Since the better hedge and safe haven properties of the Swiss Franc are likely to persist in the future, the main policy implication of the paper concerns asset allocation strategies giving relatively more weight to the Swiss currency in global stock portfolios.

Return and volatility spillover between India and leading Asian and global equity markets: an empirical analysis

PurposeThe study uses the multivariate GARCH-BEKK model (which was first proposed by Baba et al. (1990) and then further developed by Engle and Kroner (1995)) to examine the return and volatility spillover between India and four leading Asian (namely, China, Japan, Singapore and Hong Kong) and two global (namely, the United Kingdom and the United States) equity markets.Design/methodology/approachThe study employs a multivariate GARCH-BEKK model to quantify return correlation and volatility transmission across the pre- and post-2008 global financial crisis periods (apart from other conventional time series modelling like cointegration, Granger causality using vector error correction model (VECM)).FindingsThe results show a tendency of the Indian stock market index to move along with the US and Hong Kong market indices. The decrease in the value of the co-integration coefficient during the recession was explained by reduced investor confidence in developing countries. The result further shows a clear distinction in terms of volatility spillover between the Asian market vis-a-vis US and UK markets. Volatility transmission from India to Asian markets was found to be significantly higher as compared to the US and UK. So also, the study’s results show a puzzling result giving us comparable co-integration ranks for phase 2 (expansion) and phase 3 (slow-down) of the business cycle in most cases.Research limitations/implicationsIn Granger causality testing, the results were unable to ascertain the difference between phase 2 (expansion) and phase 3 (slowdown). However, the multivariate GARCH (MGARCH)-BEKK model showed a clear reduction in volatility transmission to NIFTY50 (is the flagship index on the National Stock Exchange of India Ltd. (NSE)) as India entered slow-down. This shows that the Indian economy does go through different business cycles, and the changes in parameters hence prove hypothesis 3 to be true with respect to volatility transmission to India from International markets.Originality/valueThe results show that for all countries, the volatility transmitted to India increases significantly going from phase 1 (recession) to phase 2 (expansion) and reduces again once the countries enter slow-down in phase 3 (slowdown). This shows that during expansion shocks and impulses in international markets affect the Indian markets significantly, supporting the increase in co-integration in phase 2 (expansion). During expansion, developing markets like India become profitable for investors, due to the high growth rate when compared to developed countries. This implies that a significant amount of capital enters Indian markets, which is susceptible to the volatility of international markets. The volatility transmission from India to the US and UK was insignificant in phase 1 (recession and recovery) and phase 3 (slow-down) showing a weak linkage between the markets during volatile time periods.

Dynamic comparison of portfolio risk: Clean vs dirty energy

This paper analyses whether investing in clean energy significantly worsens the risk level of investors. To that aim, we propose a dynamic strategy to carry out a comparative risk analysis of three minimum-variance portfolios: a portfolio made up exclusively of dirty energies, a portfolio made up only of clean energy assets, and a portfolio combined with the two types of energies. To that aim, we use multivariate GARCH models, concretely Asymmetric Dynamic Conditional Correlations models (ADCC-GARCH) to predict the variance and covariance matrices of the daily asset returns and we compare the portfolio volatilities using the methodology proposed by Engle and Colacito (2006). The analysed period was from January 2010 to September 2021, so that the data include half of phase II, full phase III and the onset of phase IV of the EU ETS, as well as the Brexit and COVID-19 outbreaks in the European context. Our results show that, unlike what happened in other economic crises (subprime, Brexit), from the pandemic crisis, the investment in clean energies is preferable to fossil energies, not only in terms of profitability, as other studies have shown, but also in terms of risk. Therefore, investing in clean energy companies, which are aligned with their role towards socially responsible initiatives, is valuable not only for its contribution to a sustainable energy transition to renewable sources but also for the attractiveness from a financial point of view.

Contagion effect of migration fear in pre and European refugee’s crisis period: evidence from multivariate GARCH and wavelet empirical analysis

To test the contagion effect of fear migration between countries, and to show its causality direction, our paper contributes to the economic literature by providing a new study based on migration fear indices quarterly data of France, Germany, United Kingdom and United States spanning period 1990–2019. Our empirical strategy is based on dynamic conditional correlation GARCH model and continuous wavelet transform analysis. Our results show a significant contagion effect of fear migration between the selected countries in pre and at the European Refugees crisis. The main findings of this work are changes level of conditional correlation in the two subsample periods, and changes in the arrow’s directions in red space of the phase difference between each two fear migration series. These findings indicate that European Refugees crisis changes the relationship between European Union countries and USA, and the Brexit changes the European people behavior towards migrants and refugees. Our findings offer a new directions and tracks in the international relations to the policy makers, moreover it calls into question the various studies examining economic interdependence and the contagion effect of financial crises and policies events on the different markets.

Portmanteau test for a class of multivariate asymmetric power GARCH model

We establish the asymptotic behaviour of the sum of squared residuals autocovariances and autocorrelations for the class of multi‐variate power transformed asymmetric models. We then derive a portmanteau test. We establish the asymptotic distribution of the proposed statistics. These asymptotic results are illustrated by Monte Carlo experiments. An application to a bivariate real financial data is also proposed.

DCC- and DECO-HEAVY: Multivariate GARCH models based on realized variances and correlations

This paper introduces the scalar DCC-HEAVY and DECO-HEAVY models for conditional variances and correlations of daily returns based on measures of realized variances and correlations built from intraday data. Formulas for multi-step forecasts of conditional variances and correlations are provided. Asymmetric versions of the models are developed. An empirical study shows that in terms of forecasts the scalar HEAVY models outperform the scalar BEKK-HEAVY model based on realized covariances and the scalar BEKK, DCC, and DECO multivariate GARCH models based exclusively on daily data.