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Root-n-consistent estimation of weak fractional cointegration

Hualde, J. and Robinson, Peter M. (2006) Root-n-consistent estimation of weak fractional cointegration. EM/06/499. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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Identification Number: EM/06/499

Abstract

Empirical evidence has emerged of the possibility of fractional cointegration such that the gap, β, between the integration order δ of observable time series, and the integration order γ of cointegrating errors, is less than 0.5. This includes circumstances when observables are stationary or asymptotically stationary with long memory (so δ < 1/2), and when they are nonstationary (so δ 1/2). This “weak cointegration” contrasts strongly with the traditional econometric prescription of unit root observables and short memory cointegrating errors, where β = 1. Asymptotic inferential theory also differs from this case, and from other members of the class β > 1/2, in particular ≥ n - consistent and asymptotically normal estimation of the cointegrating vector ν is possible when β < 1/2, as we explore in a simple bivariate model. The estimate depends on γ and δ or, more realistically, on estimates of unknown γ and δ. These latter estimates need to be n - consistent , and the asymptotic distribution of the estimate of ν is sensitive to their precise form. We propose estimates of γ and δ that are computationally relatively convenient, relying on only univariate nonlinear optimization. Finite sample performance of the methods is examined by means of Monte Carlo simulations, and several applications to empirical data included.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2006 the author
Subjects: H Social Sciences > HB Economic Theory
JEL classification: C - Mathematical and Quantitative Methods > C3 - Econometric Methods: Multiple; Simultaneous Equation Models; Multiple Variables; Endogenous Regressors > C32 - Time-Series Models
Sets: Collections > Economists Online
Departments > Economics
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Date Deposited: 28 Apr 2008 16:00
Last Modified: 01 Oct 2010 08:52
URI: http://eprints.lse.ac.uk/id/eprint/4542

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