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Energy and agricultural commodities and markets have been examined extensively, albeit separately, for a number of years. In the energy literature, the returns, volatility and volatility spillovers (namely, the delayed effect of a returns shock in one asset on the subsequent volatility or covolatility in another asset), among alternative energy commodities, such as oil, gasoline and ethanol across different markets, have been analysed using a variety of univariate and multivariate models, estimation techniques, data sets, and time frequencies. A similar comment applies to the separate theoretical and empirical analysis of a wide range of agricultural commodities and markets. Given the recent interest and emphasis in bio-fuels and green energy, especially bio-ethanol, which is derived from a range of agricultural products, it is not surprising that there is a topical and developing literature on the spillovers between energy and agricultural markets. Modelling and testing spillovers between the energy and agricultural markets has typically been based on estimating multivariate conditional volatility models, specifically the Baba, Engle, Kraft, and Kroner (BEKK) and dynamic conditional correlation (DCC) models. A serious technical deficiency is that the Quasi-Maximum Likelihood Estimates (QMLE) of a Full BEKK matrix, which is typically estimated in examining volatility spillover effects, has no asymptotic properties, except by assumption, so that no valid statistical test of volatility spillovers is possible. Some papers in the literature have used the DCC model to test for volatility spillovers. However, it is well known in the financial econometrics literature that the DCC model has no regularity conditions, and that the QMLE of the parameters of DCC has no asymptotic properties, so that there is no valid statistical testing of volatility spillovers. The purpose of the paper is to evaluate the theory and practice in testing for volatility spillovers between energy and agricultural markets using the multivariate Full BEKK and DCC models, and to make recommendations as to how such spillovers might be tested using valid statistical techniques. Three new definitions of volatility and covolatility spillovers are given, and the different models used in empirical applications are evaluated in terms of the new definitions and statistical criteria.

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroscedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present article marries these two strands of literature to deliver improved estimation of large dynamic covariance matrices. Supplementary material for this article is available online.

To date, most functional Magnetic Resonance Imaging (fMRI) studies have assumed that the functional connectivity (FC) between time series from distinct brain regions is constant across time. However, recently, there has been an increased interest in quantifying possible dynamic changes in FC during fMRI experiments, as it is thought that this may provide insight into the fundamental workings of brain networks. In this work we focus on the specific problem of estimating the dynamic behavior of pair-wise correlations between time courses extracted from two different regions of the brain. We critique the commonly used sliding-window technique, and discuss some alternative methods used to model volatility in the finance literature that could also prove to be useful in the neuroimaging setting. In particular, we focus on the Dynamic Conditional Correlation (DCC) model, which provides a model-based approach towards estimating dynamic correlations. We investigate the properties of several techniques in a series of simulation studies and find that DCC achieves the best overall balance between sensitivity and specificity in detecting dynamic changes in correlations. We also investigate its scalability beyond the bivariate case to demonstrate its utility for studying dynamic correlations between more than two brain regions. Finally, we illustrate its performance in an application to test–retest resting state fMRI data. •We investigate a variety of methods for estimating dynamic pair-wise correlations.•We show that the sliding-window technique can give rise to spurious results.•We propose the Dynamic Conditional Correlation (DCC) model as an alternative.•This provides a model-based approach towards estimating dynamic correlations.•DCC outperforms other methods in simulation studies.

A new covariance matrix estimator is proposed under the assumption that at every time period all pairwise correlations are equal. This assumption, which is pragmatically applied in various areas of finance, makes it possible to estimate arbitrarily large covariance matrices with ease. The model, called DECO, involves first adjusting for individual volatilities and then estimating correlations. A quasi-maximum likelihood result shows that DECO provides consistent parameter estimates even when the equicorrelation assumption is violated. We demonstrate how to generalize DECO to block equicorrelation structures. DECO estimates for U.S. stock return data show that (block) equicorrelated models can provide a better fit of the data than DCC. Using out-of-sample forecasts, DECO and Block DECO are shown to improve portfolio selection compared to an unrestricted dynamic correlation structure.

This study examines the market for green bonds, which have been in the spotlight as an eco-friendly investment product. We analyze the volatility dynamics and spillovers between the equity and green bond markets. As the return dynamics of financial products typically exhibit asymmetric volatility, we check whether green bonds also share this property. Our analyses confirm that although green bonds do exhibit the asymmetric volatility phenomenon, their volatility, unlike that of equity, is also sensitive to positive return shocks. An analysis of the association between the green bond and equity markets confirms that although the two markets have some volatility spillover effects, neither responds significantly to negative shocks in the other market.

Given the dynamic nature of the human brain, there has been an increasing interest in investigating short-term temporal changes in functional connectivity, also known as dynamic functional connectivity (dFC), i.e., the time-varying inter-regional statistical dependence of blood oxygenation level-dependent (BOLD) signal within the constraints of a single scan. Numerous methodologies have been proposed to characterize dFC during rest and task, but few studies have compared them in terms of their efficacy to capture behavioral and clinically relevant dynamics. This is mostly due to lack of a well-defined ground truth, especially for rest scans. In this study, with a multitask dataset (rest, memory, video, and math) serving as ground truth, we investigated the efficacy of several dFC estimation techniques at capturing cognitively relevant dFC modulation induced by external tasks. We evaluated two framewise methods (dFC estimates for a single time point): dynamic conditional correlation (DCC) and jackknife correlation (JC); and five window-based methods: sliding window correlation (SWC), sliding window correlation with L1-regularization (SWC_L1), a combination of DCC and SWC called moving average DCC (DCC_MA), multiplication of temporal derivatives (MTD), and a variant of jackknife correlation called delete-d jackknife correlation (dJC). The efficacy is defined as each dFC metric's ability to successfully subdivide multitask scans into cognitively homogenous segments (even if those segments are not temporally continuous). We found that all window-based dFC methods performed well for commonly used window lengths (WL ≥ 30sec), with sliding window methods (SWC, SWC_L1) as well as the hybrid DCC_MA approach performing slightly better. For shorter window lengths (WL ≤ 15sec), DCC_MA and dJC produced the best results. Neither framewise method (i.e., DCC and JC) led to dFC estimates with high accuracy. •Efficacy of 7 dynamic functional connectivity (dFC) metrics is evaluated.•Moving average dynamic conditional correlation shows best overall efficacy.•All window-based dFC metrics show high efficacy with window lengths ≥ 30sec.•Framewise (single time point) dFC metrics show low efficacy.

Against the rapid developments in cross-border investment that shed light on portfolio diversification opportunities, this study investigates the relationship between Indonesia’s sustainable ethical stocks and global sustainable financial assets. Amid market uncertainty, the need for safe havens and diversification of investment portfolios is imperative. Given the remarkable performance of Indonesia’s Islamic stocks, which are considered ethical stock, and the importance of sustainable stocks, this study examines how global financial assets such as Green Bonds, Artificial Intelligence (AI) stocks, and clean cryptocurrencies are interconnected. Employing a Dynamic Conditional Correlation – Generalized Autoregressive Heteroskedasticity (DCC-GARCH) model within the Structural Vector Autoregression (SVAR) framework, this study examined daily data spanning January 2, 2020, to August 6, 2023. This study finds strong evidence of dynamic relationships across assets, implying limited diversification benefits in the market. The results show that Cardano, as a clean cryptocurrency, can serve as a short-term safe haven, while the Green Bond potential is a long-term safe haven against Indonesia’s Islamic stocks. However, green bonds, Cardano, and AI stocks are suggested as potential diversifiers for sustainable stocks. Understanding these dynamics offers valuable insights into asset selection and diversification strategies, particularly for investors focusing on sustainable ethical assets.

The paper investigates the estimation of a wide class of multivariate volatility models. Instead of estimating an m-multivariate volatility model, a much simpler and numerically efficient method consists in estimating m univariate generalized auto-regressive conditional heteroscedasticity type models equation by equation in the first step, and a correlation matrix in the second step. Strong consistency and asymptotic normality of the equation-by-equation estimator are established in a very general framework, including dynamic conditional correlation models. The equation-by-equation estimator can be used to test the restrictions imposed by a particular multivariate generalized auto-regressive conditional heteroscedasticity specification. For general constant conditional correlation models, we obtain the consistency and asymptotic normality of the two-step estimator. Comparisons with the global method, in which the model parameters are estimated in one step, are provided. Monte Carlo experiments and applications to financial series illustrate the interest of the approach.

The study examines the role China plays compared with the US in transmitting contagion to South Asia. Trade intensity, economic downturns, and negative net equity capital outflows positively influence dynamic conditional correlations between South Asian and US/Chinese financial stock returns. Chinese and US financial firms transmitted more spillovers than they received during the global financial crisis. Results are robust to the use of USD or local currency returns, and the alternative specification of the Diebold–Yilmaz model. The role of Chinese financial firms in transmitting shocks to South Asia may be of interest to policymakers, regulators, and other market participants.