This paper proposes a novel extension of log and exponential GARCH models, where time-varying parameters are approximated by orthogonal polynomial systems. These expansions enable us to add and study the effects of market-wide and external international shocks on the volatility forecasts and...

In this article we employ certain techniques in divided differences to relate the generalized Stieltjes transform of the distribution of a randomly weighted average of independent random variables X1,…,Xm to the generalized Stieltjes transforms of the distribution functions F1,…,Fm;...