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...

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta^{-d}u_{t}, where d in (-1/2,1/2) is the fractional integration parameter and u_{t} is weakly dependent. The classical condition is existence of qmax(2,(d+1/2)^{-1}) moments...

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...

We consider the nonstationary fractional model dXt = "t with "t i.i.d.(0;2) and d 1/2. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of d conditional on initial values, and we discuss the role of the initial values for the bias....

In a recent paper Hualde and Robinson (2011) establish consistency and asymptotic normality for conditional sum-of-squares estimators, which are equivalent to conditional quasi-maximum likelihood estimators, in parametric fractional time series models driven by conditionally homoskedastic...

The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper in-troduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained...

We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and...

Few authors have studied, either asymptotically or in finite samples, the size and power of seasonal unit root tests when the data generating process [DGP] is a non-stationary alternative aside from the seasonal random walk. In this respect, Ghysels, lee and Noh (1994) conducted a simulation...