Abstract

http://ssrn.com/abstract=1612765
 
 

Citations (3)



 


 



Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model


Morten Ørregaard Nielsen


Queen's University - Department of Economics

Soren Johansen


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

May 18, 2010

Univ. of Copenhagen Dept. of Economics Discussion Paper No. 10-15

Abstract:     
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 β′X(t) is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d₀≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d₁ for any d₁≥d₀. To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

Number of Pages in PDF File: 45

Keywords: cofractional processes, cointegration rank, fractional cointegration, likelihood inference, vector autoregressive model

JEL Classification: C32

working papers series





Download This Paper

Date posted: May 21, 2010  

Suggested Citation

Nielsen, Morten Ørregaard and Johansen, Soren, Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model (May 18, 2010). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 10-15. Available at SSRN: http://ssrn.com/abstract=1612765 or http://dx.doi.org/10.2139/ssrn.1612765

Contact Information

Morten Ørregaard Nielsen (Contact Author)
Queen's University (Canada) - Department of Economics ( email )
99 University Avenue
Kingston K7L 3N6, Ontario
Canada
HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/
Soren Johansen
University of Copenhagen - Department of Economics ( email )
Copenhagen University Library
Licenssekretariatet Nørre Alle 49
DK-2200 Copenhagen N.
Denmark
Aarhus University - CREATES ( email )
Nordre Ringgade 1
Aarhus, DK-8000
Denmark
Feedback to SSRN


Paper statistics
Abstract Views: 204
Downloads: 19
Citations:  3

© 2014 Social Science Electronic Publishing, Inc. All Rights Reserved.  FAQ   Terms of Use   Privacy Policy   Copyright   Contact Us
This page was processed by apollo1 in 0.344 seconds