Supplementary Information Files for A three-dimensional asymmetric power HEAVY model

Supplementary Information Files for A three-dimensional asymmetric power HEAVY model<br>This article proposes the three‐dimensional HEAVY system of daily, intra‐daily, and range‐based volatility equations. We augment the bivariate model with a third volatility metric, the Garman–Klass estimator, and enrich the trivariate system with power transformations and asymmetries. Most importantly, we derive the theoretical properties of the multivariate asymmetric power model and explore its finite‐sample performance through a simulation experiment on the size and power properties of the diagnostic tests employed. Our empirical application shows that all three power transformed conditional variances are found to be significantly affected by the powers of squared returns, realized measure, and range‐based volatility as well. We demonstrate that the augmentation of the HEAVY framework with the range‐based volatility estimator, leverage and power effects improves remarkably its forecasting accuracy. Finally, our results reveal interesting insights for investments, market risk measurement, and policymaking.<br>