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...

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 ß for which...

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...

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...

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...

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...

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model, based on the Gaussian likelihood conditional on initial values. We give conditions on the parameters such that the process X_{t} is fractional of order d and cofractional of order d-b;...

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...

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...