This paper proves consistency and asymptotic normality for the conditional-sum-of-squares (CSS) estimator in fractional time series models. The models are parametric and quite general. The novelty of the consistency result is that it applies to an arbitrarily large set of admissible parameter...

This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with...

We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to...