A new structural multivariate GARCH-BEKK Model: Causality of green, sustainable and fossil energy ETFs

Abstract

The article examines exchange-traded funds (ETFs) for green and sustainable energy regarding causality in their asset returns and volatilities. The structural vector autoregressive (VAR) model is one of the popular methodologies for the empirical analysis of macroeconomics and finance. However, the analysis is limited to the conditional mean, and excludes the structural analysis of conditional covariance models which measure the volatility and co-volatility of the financial asset returns. In order to accommodate this limitation, we develop a new structural multivariate GARCH-BEKK model that accommodates a dimension reduction for a BEKK-type parameterization of the time-varying covariance structure. We use a quasi-maximum likelihood estimator, which is shown to have consistency and asymptotic normality. For energy ETF returns, we construct the structural GARCH-BEKK model in order to investigate the causality in returns and volatility via statistical tests and impulse response functions, especially for two events, namely a drop in crude oil prices on May 5, 2011, and the Fukushima nuclear disaster on March 11, 2011. Our empirical results have found that for the portfolio renewable energy ETFs, Solar, Wind, and Water seem to exhibit indirect mutual causality effects in mean, and direct mutual causality effects in the second moment. When we incorporate the oil market into the renewable energy market, Oil seems to dominate the causality effects, so indirect uni- causality effects of the mean from the Oil to the Solar ETF, or Oil to the Water ETF, are found. However, there are no uni-causality or mutual causality effects in the second moment.