We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=Δ^(-d)u(t), where d є (-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 of the...

We consider the nonstationary fractional model Delta^d Xt = epsilon t with epsilon t i.i.d.(0;sigma^2) and d 1/2. We derive an analytical expression for the main term of the asymptotic biasof the maximum likelihood estimator of d conditional on initial values, and we discussthe role of the...

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which...

This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d – b; where d ≥ b 1/2 are parameters to be estimated. We model the data X, …, Xт given the...

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 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 q≥2 and q1/(d+1/2)...

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...

We consider the nonstationary fractional model $\Delta^{d}X_{t}=\varepsilon _{t}$ with $\varepsilon_{t}$ i.i.d.$(0,\sigma^{2})$ and $d1/2$. 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...

In this paper we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter, d, in a nonstationary fractional time series model. The CSS estimator is...