In this article we derive convenient representations for the cumulative impulse response function of the long memory GARCH(p,d,q) (LMGARCH) process. Our results extend the results in Baillie et al. (1996) on the first order LMGARCH. Using the derived impulse response functions we compare the...

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...</2>

We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the mean and volatility dynamics, including the...