A new simulation-based prediction limit that improves on any given estimative d-step-ahead prediction limit for a Markov process is described. This improved prediction limit can be found with almost no algebraic manipulations. Nonetheless, it has the same asymptotic coverage properties as the Barndorff-Nielsen and Cox [Inference and Asymptotics (1994) Chapman and Hall, London] and Vidoni [Journal of Time Series Analysis Vol. 25, pp. 137-154.] (2004) improved prediction limits. The new simulation-based prediction limit is ideally suited to those Markov process models for which the algebraic manipulations required for the latter improved prediction limits are very complicated. We illustrate the new method by applying it in the context of one-step-ahead prediction for a zero-mean Gaussian AR(2) process and an ARCH(2) process. Copyright 2007 The Authors

No abstract

A risk measure commonly used in financial risk management, namely, Value-at-Risk (VaR), is studied. In particular, we find a VaR forecast for heteroscedastic processes such that its (conditional) coverage probability is close to the nominal. To do so, we pay attention to the effect of estimator variability such as asymptotic bias and mean square error. Numerical analysis is carried out to illustrate this calculation for the Autoregressive Conditional Heteroscedastic (ARCH) model, an observable volatility type model. In comparison, we find VaR for the latent volatility model i.e., the Stochastic Volatility Autoregressive (SVAR) model. It is found that the effect of estimator variability is significant to obtain VaR forecast with better coverage. In addition, we may only be able to assess unconditional coverage probability for VaR forecast of the SVAR model. This is due to the fact that the volatility process of the model is unobservable.

This paper aims to compare the safe-haven roles of gold and Bitcoin for energy commodities, including oils and petroleum, during COVID-19. Specifically, we examine the presence of reduction in downside risk after mixing gold/Bitcoin with such energy commodities. To do this, we account for dependence among energy commodities and gold/Bitcoin returns by applying a (vine) copula. The findings show that gold substantially reduces the downside risk of a portfolio containing any allocation to gold and energy commodities, indicating its safe-haven ability. In contrast, Bitcoin’s safe-haven functionality is inconsistent since the downside risk reduction is achieved for Bitcoin’s small allocation only.

No abstract