Title: A robust estimation and testing of the cointegration order based on the frequency domain
Authors: Igor Souza - Universidade Federal de Minas Gerais (Brazil) [presenting]
Valderio Anselmo Reisen - DEST-CCE-UFES (Brazil)
Pascal Bondon - CentraleSupelec (France)
Glaura Franco - Universidade Federal de Minas Gerais (Brazil)
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 by using periodogram based on $M$-regression method with Huber function. 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 are derived and consistency properties were also obtained. The asymptotic normality of the estimator, under Gaussian and non-Gaussian innovations, were also established. Performance is investigated using Monte Carlo simulations under two scenarios: series uncontaminated and contaminated with additive outliers.