Time-varying Correlation Research Articles

Modelling Multivariate Return Volatilities by Independent Components Using Johnson SU Likelihood

Time-varying volatility modelling is crucial in financial econometrics. For multivariate data, time-varying correlations across securities are important to explain the co-movement of the data. Therefore, we need to estimate the covariance matrix. Estimating a large conditional covariance matrix requires the estimation of a large number of parameters, which is a hard task and often leads to convergence difficulties in the estimation algorithm. We introduce a framework for forecasting the conditional covariance matrix of a large data set by employing a factor model to reduce dimensionality, with the factors estimated using independent components. The main contribution of our article is the estimation of the unobserved independent components using Johnson SU likelihood, which captures the skewness and excess kurtosis—stylized facts in stock returns. First, we extract the independent components using the Johnson SU distribution, maximizing their non-Gaussianity. Second, we sorted the independent components in terms of their explained variability and fit a univariate GARCH process on a few common independent components. Next, we approximate the conditional covariance matrix of the data through a linear combination of the conditional variances of those select few independent components. We apply this procedure to 50 stock returns data (listed in Nifty 50) that exhibit excess kurtosis and skewness, and the findings show that our methodology dominates other algorithms in extracting the independent components. This method enables fund managers to accurately forecast a large conditional covariance matrix, facilitating effective risk management and portfolio construction.

Time–Frequency Co-Movement of South African Asset Markets: Evidence from an MGARCH-ADCC Wavelet Analysis

The growing prominence of generating a well-diversified portfolio by holding securities from multi-asset markets has, over the years, drawn criticism. Various financial market events have caused asset markets to co-move, especially in emerging markets, which reduces portfolio diversification and enhances return losses. Consequently, this study examines the time–frequency co-movement of multi-asset classes in South Africa by using the Multivariate Generalized Autoregressive Conditional Heteroscedastic–Asymmetrical Dynamic Conditional Correlation (MGARCH-DCC) model, Maximal Overlap Discrete Wavelet Transformation (MODWT), and the Continuous Wavelet Transform (WTC) for the period 2007 to 2024. The findings demonstrate that the equity–bond, equity–property, equity–gold, bond–property, bond–gold, and property–gold markets depict asymmetrical time-varying correlations. Moreover, correlation in these asset pairs varies at investment periods (short-term, medium-term, and long-term), with historical events such as the 2007/2008 Global Financial Crisis (GFC) and the COVID-19 pandemic causing these asset pairs to co-move at different investment periods, which reduces diversification properties. The findings suggest that South African multi-asset markets co-move, affecting the diversification properties of holding multi-asset classes in a portfolio at different investment periods. Consequently, investors should consider the holding periods of each asset market pair in a portfolio as they dictate the level of portfolio diversification. Investors should also remember that there are lead–lag relationships and risk transmission between asset market pairs, enhancing portfolio volatility. This study assists investors in making more informed investment decisions and identifying optimal entry or exit points within South African multi-asset markets.

Bayesian inference for link travel time correlation of a bus route

Estimation of link travel time correlation of a bus route is essential to many bus operation applications. Link travel time on a bus route could exhibit complex correlation structures, such as long-range correlations, negative correlations, and time-varying correlations. This paper develops a Bayesian Gaussian model to estimate the link travel time correlation matrix of a bus route using smart-card-like data. Our method overcomes the small-sample-size problem in correlation matrix estimation by borrowing/integrating those incomplete observations from other bus routes. We first conduct a synthetic experiment and results show that the proposed method produces an accurate estimation for correlations with credible intervals. Next, we perform experiments on a real-world bus route with in-out-stop record data; results show that both local and long-range correlations exist on this bus route. Finally, we demonstrate an application of using the estimated covariance matrix to make probabilistic forecasting of link and trip travel time.

Volatility spillovers and time-varying correlations across stock and commodity markets: An assessment during the epidemic crisis era

The financial and economic stability of the business world is greatly damaged by a number of crises over the years. These crises also change and affect stock markets around the globe. This study examines the nonlinear behavior of well-known stock markets in the US, Europe, Canada, and Asia (S&P 500, Nikkei 225, CAC40, DAX30, Bombay Stock Index, Hang Seng Index, and Canadian Stock Index). We also investigate the commodity indexes (Gold, Bitcoin, Brent Crude Oil, and West Texas Crude Oil). The transmission of returns and the volatility propagation pattern across stock-commodity markets during the COVID-19 era is analyzed using the VAR DCC MEGARCH model. The results demonstrate that correlations intensify and become more complicated during the COVID-19 period, especially between financial market indices and oil commodity indices. However, the volatility spillover statistics during the pandemic period show a definite rise in the uncertainty of financial market indices due to index instability. The analysis also shows that financial markets experience a substantial leverage effect during the pandemic crisis. According to the research, Bitcoin is crucial for reducing portfolio risk during the health crisis, and gold proves to be the best option for investors to diversify their financial risk.

Detection of flood trends and drivers in the Taihu Basin, China

Study regionTaihu Basin, China Study focusFloods threaten humans, the environment, economic activity, and infrastructure. In this study, a new trend test and flood-frequency methods were adopted to detect extreme floods and their distributions based on flood-event identification. To fully understand the phased process of the influence of human activities on extreme hydrological processes, 12 copula functions were employed creatively in combined static and dynamic time-varying correlation aspects between extreme precipitation and floods. New hydrological insights for the regionAlthough both significant and insignificant increasing trends of the annual maximum water level in all three hydrological districts were examined, the periodic oscillations of all the stations were similar. Thus, it was significant to fully detect the periodical variation of floods. Extreme floods occurred mainly in the 1990s, as measured by frequency estimates. Generally, the nonstationary response relationship between heavy rain and an extreme water level was gradually strengthened; that is, a certain magnitude precipitation seemed to induce a greater-intensity flood event as time passed. Through the identification of historical flood events and the analysis of the rise and fall processes of floods, we found that the main reason for variation in the response relationship was the increase in the water level before the rising stage, rather than the water level rising in the Taihu Basin. Our study findings further existing knowledge on the regional flood-control design standard and can ensure the coexistence of humans and water systems in the future.

Dynamic correlation among renewable energy, technology, and carbon markets: Evidence from a novel nonparametric time-frequency approach

In addressing the challenges of energy security and climate change, ongoing efforts involve the development of innovative technologies to support the shift from conventional to clean energy sources. Concurrently, the establishment of carbon markets aims to facilitate a decrease in carbon emissions by enabling the trade of carbon credits. This study adds to the energy-climate discussion by examining the evolving dynamics of returns on investments in renewable energy, technology, and carbon markets. Specifically, the time-varying correlation among renewable energy, technology, and carbon markets in the European Union is examined from September 18, 2017 to December 14, 2022. The techniques employed for empirical analyses are the nonparametric time-frequency, Benjamini-Hochberg, and Benjamini-Yekutieli correlation techniques, as well as the time-varying Granger causality. Highlights from the results are as follows. Renewable energy, technology, and carbon markets exhibit time and frequency variations in their relationships, with significant correlations notably present during periods marked by major shifts in energy policy. Secondly, renewable energy and carbon markets exhibit very weak or even absent correlation, indicating their suitability for portfolio diversification. Furthermore, investors could benefit significantly by including both technology and carbon markets in their portfolios to reduce overall risk. Several additional recommendations are also provided in this study.

Transient surface pressure of a rectangular cylinder subjected to downburst-like winds

Thunderstorm downbursts are transient in nature and have been responsible for a variety of structural damages in recent years. Currently, the researchers have done several works on the characteristics of downburst wind speed. Nonetheless, rare attention has been placed on the structural aerodynamics characteristics subjected to downburst winds. Based on this, an experimental investigation is performed to reproduce downburst-like winds physically and to study the transient surface pressures (SPs) on a 5:1 rectangular cylinder (RC). The experiment is conducted within a multiple-fan active control wind tunnel (MFACWT) and mainly focuses on simulating the transient characteristics of downburst-like flow, including time-varying mean (TVM) wind speed and nonstationary wind fluctuation. The resulting SPs are measured to understand the influence of transient wind on the aerodynamic behavior of bluff bodies. The spatiotemporal characteristics of the SPs are analyzed using wavelet transform and Priestley's classic spectral theory. The results indicate that the transient nature of the downburst-like flow can be physically reproduced by a MFACWT. The instantaneous pressures of a RC are illustrated by both the turbulence parameters of the transient flow and the flow-separation characteristics. The pressure coefficients normalized by the TVM of the downburst-like winds remain constant, which provides a more appropriate way to estimate the transient gust loading in a quasi-steady manner. Interestingly, the phenomenon of the time-varying phase shift and time-varying correlation of chordwise SPs is observed when the turbulent velocity changes dramatically. In addition, the normalized surface pressure can be regarded as a stationary stochastic process, which provides a significant basis for further establishing the theoretical model of nonstationary gust-loading.

Gauging force by tapping tendons? Inaccurately in the human patellar tendon

Accurately estimating in vivo tendon load non-invasively remains a major challenge in biomechanics, which might be overcome by shear-wave tensiometry. Shear-wave tensiometry measures the speed of mechanically induced tendon shear waves by skin-mounted accelerometers. To gauge the feasibility and accuracy of this novel technique, we obtained patellar tendon shear wave speeds via shear-wave tensiometry during sustained or ramp voluntary contractions of the knee extensors in two experiments (n = 8 in both). In experiment one, participants produced a constant knee extension torque of ∼ 50 Nm at five different knee joint angles (i.e. variable tendon load), which resulted in estimated patellar tendon forces between 1005 ± 6N and 1182 ± 16 N. However, wave speed squared did not correlate with estimated tendon force within participants (rrm(31) = -0.19, p = 0.278). In experiment two, averaged correlation coefficients between normalized wave speed squared and torque of maximal and submaximal voluntary contractions across participants ranged between r = 0.43 and r = 0.94, while the time-varying correlation between these normalized signals ranged from r = -0.99 to r = 1.00. Further, the mean absolute errors (MAEs) between normalized wave speed squared and normalized torque across participants ranged between 0.03 and 0.54, which were larger than the MAEs between normalized torque and normalized summed EMG amplitude from the superficial quadriceps muscles (0.03–0.54 versus 0.06–0.26, respectively). In conclusion, there was no simple relation between shear wave speed squared and patellar tendon load, which severely limits the feasibility of shear-wave tensiometry for accurately estimating in vivo tendon load at the knee joint.

Time-Varying Correlations between JSE.JO Stock Market and Its Partners Using Symmetric and Asymmetric Dynamic Conditional Correlation Models

Time-Varying Correlations between JSE.JO Stock Market and Its Partners Using Symmetric and Asymmetric Dynamic Conditional Correlation Models

Carbon Emissions Pricing: Linkages Between EU ETS Spot and Future Prices and Completeness of EU ETS Market

The study examines the relationship and linkages between spot and future prices of European Union Emission Trading Systems (EU-ETS) during 2019–2021. Dynamic conditional correlation specification of multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model was employed to examine the time-varying correlation between spot and future prices. Also, vector autoregression mean model and MGARCH-Baba-Engle-Kroner-Kraft volatility model was jointly estimated to model the spillover between EU ETS spot and future prices in the first and second moments. Lastly, we utilize the variance-covariance matrix of joint mean-variance model estimation to derive the optimal conditional hedge ratio as well as the hedge effectiveness of EU ETS future contracts. Our findings reveal a high conditional correlation and significant spillover between carbon spot and future markets in EU. Further, our study uncovers a high degree of hedge effectiveness for EU ETS future contracts. This is possibly the first study that examines the linkages between EU ETS spot and future prices pertaining to the recent transition stage of phase III and the initial stage of ongoing phase IV of the ETS market. Our findings pinpoint to ETS markets becoming more complete and in turn offering optimal hedging avenues. JEL Codes: G15, C58, Q38

Volatile safe-haven asset: Evidence from Bitcoin

Despite high volatility, Bitcoin is known to offer diversification benefits through its relatively low correlation with stock markets. Unlike traditional safe-haven assets, Bitcoin prices strongly respond to time-varying correlations and diversification benefits. We find that a decrease (an increase) in correlation between Bitcoin and S&P500 index returns strongly predicts higher (lower) Bitcoin returns the next day. Under the classical mean–variance framework, we develop a stylized model of Bitcoin prices utilizing extreme disagreement among heterogeneous Bitcoin investors. When our model is calibrated to the observed predictability of Bitcoin returns, the model simultaneously explains the lack of predictability in traditional safe-haven assets such as gold and long-term treasuries.

Volatility transmission in the property market during two inflationary periods: The 2008–2009 global financial crisis and the COVID-19 crisis

This research paper investigates the changes in correlation patterns of volatility between the UK and US property markets and other global markets during periods of inflation. We use the global financial crisis (GFC) and the COVID-19 crisis as proxies for two inflationary periods. Our data set consists of the period between April 11, 2007, to April 4, 2022. We apply a bivariate Dynamic Conditional Correlation (DCC) and a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to explain the time-varying correlation between UK and US property markets and other global property markets. According to our analysis, there is a sizable time-varying link between the real estate markets in our sample. Additionally, we discover that the GFC and COVID-19 exhibit different relationships with UK and US real estate market indices.

Is there a time-varying nexus between stock market liquidity and informational efficiency? – A cross-regional evidence

PurposeThis study aims to measure the degree of volatility comovement between stock market liquidity and informational efficiency across Asia, Europe, North-South America, Africa, and the Pacific Ocean over three decades. In particular, the authors analyze the extent of the time-varying nexus between different aspects of stock market liquidity and multifractal scaling properties of the stock return series across various regions and diversified market conditions. This study further investigates several factors altering the degree of dynamic conditional correlations (DCCs) between the efficiency and liquidity of the domestic stock markets.Design/methodology/approachThe study measures five aspects of stock market liquidity – tightness, depth, breadth, immediacy, and adjusted immediacy. The authors evaluate the multifractal scaling properties of the stock return series to measure the level of stock market efficiency across the regions and diversified market conditions. The study uses the dynamic conditional correlation-multivariate generalized autoregressive conditional heteroscedasticity framework to quantify the degree of volatility comovement between liquidity and efficiency over the period.FindingsThe study finds the presence of stronger volatility comovement between inefficiency and illiquidity due to the price impact characteristics of the stock markets irrespective of different regions and diversified market conditions. The extent of time-variation increased following the shock periods, indicating the significant role of the financial crisis in increasing the volatility comovement between inefficiency and illiquidity. The highest degree of time-varying correlation is observed in the developed stock markets of Northwestern and Northern Europe compared to the regional and emerging counterparts. On the other hand, weak DCCs are observed in the emerging stock markets of Europe.Originality/valueThe output of the present study assists investors in identifying diversification opportunities across the regions. Additionally, the study has significant implications for market regulators, aiding in predicting future troughs and peaks. The prediction, in turn, helps formulate capital market development plans during dynamic economic situations.

Unsupervised dynamic prognostics for abnormal degradation of lithium-ion battery

Lithium-ion batteries may suffer an abnormal degradation defined by a significantly accelerated performance drop after a period of linear and low-rate degradation, resulting in severe danger to operational safety and reliability. Existing supervised data-driven prognostics for abnormal degradation rely heavily on adequate high-quality training samples, thus hindering their real-world utilization. Therefore, this paper develops an unsupervised dynamic prognostics framework that is dynamically executed as the cycle number increases to provide accurate and timely warnings for abnormal degradation. In the framework, an extended asymmetric quantum clustering (EAQC) can preliminarily identify the risky battery with the abnormal degradation trend. Its use of multi-dimensional feature degradation rates and potential function for clustering makes it outperform other density-based clustering methods. Then, for the identified battery, a time-varying double-layer autoregression (TVDLAR) can accurately predict its knee point of abnormal degradation. TVDLAR produces much earlier warning than other autoregression methods, which owes to its modeling ability of the time-varying correlation in battery historical degradation data. Through applying to two experimental datasets consisting of 174 lithium-ion batteries of different types under various working conditions, the framework is proven highly effective and shows significant superiority over some alternative approaches; all abnormal degradation can be timely warned before the corresponding knee points, and the average earlier warning cycles are 86 and 116, respectively. Compared with supervised data-driven methods, the proposed unsupervised dynamic prognostics framework has the advantages of low data requirement, low computational consumption, and good interpretability, indicating its substantial potential for application.

Can fiat currencies really hedge Pax gold? Evidence from range-based DCC models

PurposeThis paper assesses the co-movement between Pax gold and six fiat currencies. It also investigates the optimal time-varying hedge ratios in order to examine the properties of Pax gold as a diversifier and hedge asset.Design/methodology/approachThis paper examines the volatility spillover between Pax gold and fiat currencies using the framework of wavelet analysis, BEKK-GARCH models and Range DCC-GARCH. Moreover, this paper proposes to use the covariance and variance structure obtained from the new range DCC-GARCH framework to estimate the time-varying optimal hedge ratios, the optimal weighs and the hedging effectiveness.FindingsWavelet coherence method reveals that, at low frequency, large zone of co-movements appears for the pairs Pax gold/EUR, Pax gold/JPY and Pax gold/RUB. Further, the BEKK results show unidirectional (bidirectional) transmission effects between Pax gold and EUR, GBP, JPY and CNY (INR, RUB) fiat currencies. Moreover, the Range DCC results show that the Pax gold and the fiat currency returns are weakly correlated with low coefficients close to zero. Thus, Pax gold seems to serve as a safe haven asset against the systematic risk of fiat currency markets. In addition, the results of optimal weights show that rational investor should invest more in Pax gold and less in fiat currencies. Concerning the hedge ratios results, the findings reveal that the INR (JPY) fiat currency appears to be the most expensive (cheapest) hedge for the Pax-gold market. However, the JPY’s fiat currency appears to be the cheapest one. As for hedging effectiveness results, the authors found that hedging strategies including fiat currencies–Pax gold pairs are most likely to sharply decrease the portfolio’s risk.Practical implicationsA comprehensive understanding of the relationship between Pax Gold and fiat currencies is crucial for refining portfolio strategies involving cryptocurrencies. This research underscores the significance of grasping volatility transmissions between these currencies, providing valuable insights to guide investors in their decision-making processes. Moreover, it encourages further exploration into the interdependencies of digital currencies. Additionally, this study sheds light on effective contagion risk management, particularly during crises such as Covid-19 and the Russia–Ukraine conflict. It underscores the role of Pax Gold as a safe-haven asset and offers practical guidance for adjusting portfolios across various economic conditions. Ultimately, this research advances our comprehension of Pax Gold’s risk-return profile, positioning it as a potential hedge during periods of uncertainty, thereby contributing to the evolving literature on cryptocurrencies.Originality/valueThis study’s primary value lies in its pioneering empirical examination of the time-varying correlations and scale dependence between Pax Gold and fiat currencies. It goes beyond by determining optimal time-varying hedge ratios through the innovative Range-DCC-GARCH model, originally introduced by Molnár (2016) and distinguished by its incorporation of both low and high prices. Significantly, this analysis unfolds within the unique context of the Covid-19 pandemic and the Russian–Ukrainian conflict, marking a novel contribution to the field.

Real-time forecast of DSGE models with time-varying volatility in GARCH form

Recent research shows that time-varying volatility plays a crucial role in non-linear modeling. Contributing to this literature, we suggest an approach that allows for straightforward computation of DSGE models with time-varying volatility, where the volatility component is formulated as a GARCH process. As an application of our approach, we examine the forecasting performance of this DSGE-GARCH model using euro area real-time data. Our findings suggest that the DSGE-GARCH approach is superior in out-of-sample forecasting performance in comparison to various other benchmarks for the forecast of inflation rates, output growth and interest rates, especially in the short term. Comparing our approach to the widely used stochastic volatility specification using in-sample forecasts, we also show that the DSGE-GARCH is superior in in-sample forecast quality and computational efficiency. In addition to these results, our approach reveals interesting properties and dynamics of time-varying correlations (conditional correlations).

Is investing in green assets costlier? Green vs. non-green financial assets

The urgent shift towards a zero- or low-carbon economy to combat climate change has heightened interest in green financial instruments among investors. Although green financial assets have grown significantly in a decade, investing in green assets is speculated to be costlier than traditional assets. Against this backdrop, we analyse whether investing in green financial assets is costlier than investing in traditional assets. We employ a comprehensive methodology, encompassing risk-adjusted returns, tail risks, time-varying correlations, novel quantile volatility connectedness, and portfolio implication techniques to show that most green assets outperform non-green assets in terms of risk-adjusted returns. Likewise, the potential loss likelihood of investing in green assets is lower. Our time-varying correlation outcomes reveal a strong positive association between green assets and their traditional counterparts, with limited hedging opportunities. Further, quantile vector autoregression results suggest that total connectedness between the green assets and their non-green pairs is lower in the normal market than in the extreme markets. Green and non-green asset pairs are also reciprocal in spreading and absorbing volatility shocks across most market states. Finally, the portfolio implications reveal that most asset pairs have a higher hedging cost; however, allocating more than 90% of funds to green assets can provide significant hedging effectiveness. Overall, investing in green assets is not costlier than investing in non-green assets, but they may be marginally rewarded. Our empirical findings have crucial implications for investors, policymakers, and regulatory bodies.

Integration of Pakistan's stock market with the stock markets of top ten developed economies

This study examines the integration of Pakistan's Stock Market with the stock markets of the top ten largest economies in the world—USA, China, Japan, Germany, the UK, India, France, Italy, Brazil, and Canada—from January 2015 to October 2020. To examine long- and short run integration, this study employed Johansen and Juselius co-integration and pair-wise Granger causality tests. In the long run, the results indicated that Pakistan's Stock Market is not integrated with these markets. This implies that the market is more attractive in portfolio diversification for international investors, and vice versa. In the short run, the results revealed that, except for China, Pakistan's stock market integrates with the remaining nine markets. However, Pakistan's stock market exhibits a bidirectional relationship with the USA, Japan, Germany, the UK, and France in the lead-lag relationship. However, its relationship with India, Italy, Brazil, and Canada is unidirectional, with Pakistan's stock market leading, while these markets are following. For Pakistani investors, China is the optimal market, and vice versa. Importantly, our findings help policymakers to comprehend Pakistan's dynamic relationship with its trading partners. To the best of our knowledge, no prior study has employed advanced techniques to address the time-varying correlation among the selected markets. By determining Pakistan's stock market integration with its trading partners, this study aimed to fill this empirical literature gap.

Estimating correlations among elliptically distributed random variables under any form of heteroskedasticity

The paper introduces a semiparametric estimator of the correlations among elliptically distributed random variables invariant to any form of heteroscedasticity, robust to outliers, and asymptotically normal. Our estimator is particularly fit for financial applications as vectors of stock returns are generally well approximated by heteroskedastic processes with elliptical (conditional) distributions and heavy tails. The superiority of our estimator with respect to Pearson's sample correlation in financial applications is illustrated using simulated data and real high-frequency stock returns. Using simple exponentially weighted moving averages, we extend our estimator to the case of time-varying correlations and compare it to the popular GARCH-DCC model. We show that the two approaches have comparable performances through simulations and a simple application. However, our estimator is extremely fast to compute, computationally robust, and straightforward to implement.

An analysis on the time-varying correlation among selected agricultural commodities: A DCC-GARCH Model-based approach

An analysis on the time-varying correlation among selected agricultural commodities: A DCC-GARCH Model-based approach