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Title: The estimation and testing of the fractional cointegration order based on the frequency domain: A robust approach Authors:  Valderio Anselmo Reisen - DEST-CCE-UFES (Brazil) [presenting]
Igor Souza - Universidade Federal de Minas Gerais (Brazil)
Glaura Franco - Universidade Federal de Minas Gerais (Brazil)
Pascal Bondon - CentraleSupelec (France)
Abstract: The aim is to estimate the degree of cointegration in bivariate series. A test statistic for the non-cointegration based on the determinant of the spectral density matrix for the frequencies close to zero is proposed. 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 $I(d-b)$, $b\in [0,d]$. The proposed estimator for $b$ is obtained by performing a regression of logged determinant on a set of logged Fourier frequencies. Under the null hypothesis of non-cointegration, 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. The robustness to the presence of outliers is also addressed using $M$-periodograms. Their performance was investigated using Monte Carlo simulations.