Unit Roots in White Noise

41 Pages Posted: 8 Jan 2010 Last revised: 7 Apr 2011

See all articles by Harald Uhlig

Harald Uhlig

University of Chicago - Department of Economics

Alexei Onatski

Columbia University, Graduate School of Arts and Sciences, Department of Economics

Date Written: March 24, 2011

Abstract

We show that the empirical distribution of the roots of the vector auto-regression of order p fitted to T observations of a general stationary or non-stationary process, converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T) /p → 0 and p³/T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated vector auto-regression will converge by absolute value to unity. For fixed p, we derive an asymptotic approximation to the expected empirical distribution of the estimated roots as T → ∞. The approximation is concentrated in a circular region in the complex plane for various data generating processes and sample sizes. (revised March 24, 2011, original version March, 2009)

Suggested Citation

Uhlig, Harald and Onatski, Alexei, Unit Roots in White Noise (March 24, 2011). MFI Working Paper No. 2009-04, Available at SSRN: https://ssrn.com/abstract=1532940 or http://dx.doi.org/10.2139/ssrn.1532940

Harald Uhlig (Contact Author)

University of Chicago - Department of Economics ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Alexei Onatski

Columbia University, Graduate School of Arts and Sciences, Department of Economics ( email )

420 W. 118th Street
New York, NY 10027
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
64
Abstract Views
578
rank
379,288
PlumX Metrics