The Limiting Distribution of the Autocorrelation Coefficient Under a Unit Root

Posted: 22 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Date Written: January 21, 2012

Abstract

The limiting distribution of the normalized autocorrelation coefficient in the case of a unit root is given in a closed form. It is found that high order transcendental functions such as the parabolic cylinder functions are indispensable to express this distribution, thus departing from the simple standard normal distribution that arises in the case of a stable root. Using the formulae derived in this paper, some numerical results available from previous studies are then extended and refined. Finally, the formulae are manipulated analytically to explain the unusual shape of the distribution.

Suggested Citation

Abadir, Karim M., The Limiting Distribution of the Autocorrelation Coefficient Under a Unit Root (January 21, 2012). Available at SSRN: https://ssrn.com/abstract=1989475

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

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