This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data...

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>