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 presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung's (2002) test as the special case d = 1. It is shown that (i) each member of the family with d 0 is consistent, (ii) the asymptotic distribution depends on d, and thus...

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...

We study the relation between realized and implied volatility in the bond market. Realized volatility is constructed from high-frequency (5-minute) returns on 30 year Treasury bond futures. Implied volatility is backed out from prices of associated bond options. Recent nonparametric statistical...

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...