Fractional Cointegration Rank Estimation

Tinbergen Institute Discussion Paper 14-021/III

33 Pages Posted: 14 Feb 2014

See all articles by Katarzyna Lasak

Katarzyna Lasak

VU Amsterdam; Tinbergen Institute

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics

Date Written: February 12, 2014


We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The first step consists in estimating the parameters of the model under the null hypothesis of the cointegration rank r=1,2,…,p-1. This step provides consistent estimates of the order of fractional cointegration, the cointegration vectors, the speed of adjustment to the equilibrium parameters and the common trends. In the second step we carry out a sup-likelihood ratio test of no-cointegration on the estimated p-r common trends that are not cointegrated under the null. The order of fractional cointegration is re-estimated in the second step to allow for new cointegration relationships with different memory. We augment the error correction model in the second step to adapt to the representation of the common trends estimated in the first step. The critical values of the proposed tests depend only on the number of common trends under the null, p-r, and on the interval of the orders of fractional cointegration b allowed in the estimation, but not on the order of fractional cointegration of already identified relationships. Hence this reduces the set of simulations required to approximate the critical values, making this procedure convenient for practical purposes. In a Monte Carlo study we analyze the finite sample properties of our procedure and compare with alternative methods. We finally apply these methods to study the term structure of interest rates.

Keywords: Error correction model, Gaussian VAR model, Likelihood ratio tests, Maximum likelihood estimation

JEL Classification: C12, C15, C32

Suggested Citation

Lasak, Katarzyna and Velasco, Carlos, Fractional Cointegration Rank Estimation (February 12, 2014). Tinbergen Institute Discussion Paper 14-021/III. Available at SSRN: or

Katarzyna Lasak (Contact Author)

VU Amsterdam ( email )

Department of Econometrics, FEWEB
De Boelelaan 1105
Amsterdam, 1081 HV

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics ( email )

Calle Madrid 126
Getafe, 28903
+34-91 6249646 (Phone)
+34-91 6249875 (Fax)

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