The Estimation and Testing of the Cointegration Order Based on the Frequency Domain |
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Authors: | Igor Viveiros Melo Souza Valderio Anselmo Reisen Glaura da Conceição Franco Pascal Bondon |
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Affiliation: | 1. DEECO, UFOP and Departamento de Estatística, UFMG, Rua do Catete, no. 166 Mariana, Minas Gerais 30420-000, Brazil (igorviveiros@gmail.com);2. Departamento de Estatística, PPGECON, PPGEA, UFES, Av. Fernando Ferrari s/n Goiabeiras, Vitoria, Espírito Santo 29060-900, Brazil (valderioanselmoreisen@gmail.com);3. Departamento de Estatística, UFMG, Av. Antonio Carlos, no. 6627 Predio do ICEx 4067 Belo Horizonte, Minas Gerais 31270-901, Brazil (glaura@est.ufmg.br);4. Laboratoire des Signaux et Systèmes, CNRS - CentraleSupélec Université Paris-Sud, France (bondon@lss.supelec.fr |
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Abstract: | ABSTRACTThis article proposes a method to estimate the degree of cointegration in bivariate series and suggests a test statistic for testing noncointegration based on the determinant of the spectral density matrix for the frequencies close to zero. In the study, series are assumed to be I(d), 0 < d ? 1, with parameter d supposed to be known. In this context, the order of integration of the error series is I(d ? b), b ∈ [0, d]. Besides, the determinant of the spectral density matrix for the dth difference series is a power function of b. The proposed estimator for b is obtained here performing a regression of logged determinant on a set of logged Fourier frequencies. Under the null hypothesis of noncointegration, the expressions for the bias and variance of the estimator were derived and its consistency property was also obtained. The asymptotic normality of the estimator, under Gaussian and non-Gaussian innovations, was also established. A Monte Carlo study was performed and showed that the suggested test possesses correct size and good power for moderate sample sizes, when compared with other proposals in the literature. An advantage of the method proposed here, over the standard methods, is that it allows to know the order of integration of the error series without estimating a regression equation. An application was conducted to exemplify the method in a real context. |
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Keywords: | Consistency Determinant of spectral density matrix Estimator Fractional cointegration Test of noncointegration |
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