In this article we derive conditions which ensure the non-negativity of the conditional variance in the Hyperbolic GARCH(p, d, q) (HYGARCH) model of Davidson (2004). The conditions are necessary and sufficient for p ≤ 2 and sufficient for p > 2 and emerge as natural extensions of the inequality constraints derived in Nelson and Cao (1992) for the GARCH model and in Conrad and Haag (2006) for th...

Dans cet article, nous proposons un modele hyperbolique GARCH realise adaptatif (ARealized HYGARCH) pour modeliser la longue memoire des series chronologiques a haute frequence avec d’eventuelles changements de regimes. Le changement regime est modelise, en permettant l’intercepte suivre une forme fonction lisse et flexible introduite par Gallant. De plus, les conditions stabilite ce sont etabl...

South Africa is a cornucopia of the platinum group metals particularly platinum and palladium. These metals have many unique physical and chemical characteristics which render them indispensable to technology and industry, the markets and the medical field. In this paper we carry out a holistic investigation on long memory (LM), structural breaks and stylized facts in platinum and palladium ret...

In this study, we analyse the implications of clean energy, oil and emission prices for energy sector stock in GCC region. so doing, estimate one-day-ahead value at risk (VaR) expected shortfall (ES) Saudi, Abu Dhabi Kuwaiti over short long trading positions using three different memory Autoregressive conditional heteroskedasticity (ARCH)/ Generalized(G)- ARCH models: fractionally integrated as...

This paper analyses moment and near-epoch dependence properties for the general class of models in which the conditional variance is a linear function of squared lags of the process. It is shown how the properties of these processes depend independently on the sum and rate of convergence of the lag coefficients, the former controlling the existence of moments, and the latter the memory of the v...

a r t i c l e i n f o Due to the connections of energy uses, carbon emissions and climate, this study investigates the interactions, volatility spillovers, and long memory effects for carbon, oil, natural gas and coal markets by using FIEC-HYGARCH model. It also discusses the mediating effect of extreme weather. The empirical results verify that the FIEC-HYGARCH model can capture the long-term ...