The Estimation and Testing of the Cointegration Order Based on the Frequency Domain. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Souza, Igor Viveiros Melo; Reisen, Valderio Anselmo; Franco, Glaura da Conceição; Bondon, Pascal
• Is Part Of: Journal of business & economic statistics. Volume 36:Issue 4(2018)
• Page Start: 695
• Page End: 704
• Publication Date: 2018-10-02
• Subjects: Consistency -- Determinant of spectral density matrix -- Estimator -- Fractional cointegration -- Test of noncointegration; Economics -- Statistical methods -- Periodicals; Commercial statistics -- Periodicals; Économie politique -- Méthodes statistiques -- Périodiques; Statistique commerciale -- Périodiques; 330.015195
• DOI: 10.1080/07350015.2016.1251442
• Languages: English
• ISSNs: 0735-0015

Abstract

ABSTRACT: This 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 d th 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.