The Role of Initial Values in Nonstationary Fractional Time Series Models

30 Pages Posted: 15 Nov 2012

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Morten Ørregaard Nielsen

Queen's University - Department of Economics

Date Written: November 8, 2012

Abstract

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 bias of the maximum likelihood estimator of d conditional on initial values, and we discuss the role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given.

Keywords: Asymptotic expansion, bias, conditional inference, fractional integration, initial values, likelihood inference

JEL Classification: C22

Suggested Citation

Johansen, Soren and Nielsen, Morten Orregaard, The Role of Initial Values in Nonstationary Fractional Time Series Models (November 8, 2012). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 12-18, Available at SSRN: https://ssrn.com/abstract=2175574 or http://dx.doi.org/10.2139/ssrn.2175574

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Morten Orregaard Nielsen

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario
Canada

HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/

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