Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/67797
Authors: 
Johansen, Søren
Nielsen, Morten Ørregaard
Year of Publication: 
2008
Series/Report no.: 
Queen's Economics Department Working Paper 1172
Abstract: 
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 X_{1},...,X_{T} given the initial values X_{-n}, n = 0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including d and b, and prove that they converge in distribution. We use the results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2 < b < d < inf.}, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis. The limit distributions contain the fractional Brownian motion of type II.
Subjects: 
Dickey-Fuller test
fractional unit root
likelihood inference
JEL: 
C22
Document Type: 
Working Paper

Files in This Item:
File
Size
345.76 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.