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Econometrics 2016, 4(4), 49; doi:10.3390/econometrics4040049

Testing for the Equality of Integration Orders of Multiple Series

1
Department of Finance, Donghua University, Shanghai 200051, China
2
Department of Statistics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
*
Author to whom correspondence should be addressed.
Academic Editor: Pierre Perron
Received: 15 July 2016 / Revised: 23 November 2016 / Accepted: 25 November 2016 / Published: 15 December 2016
(This article belongs to the Special Issue Unit Roots and Structural Breaks)
View Full-Text   |   Download PDF [265 KB, uploaded 15 December 2016]

Abstract

Testing for the equality of integration orders is an important topic in time series analysis because it constitutes an essential step in testing for (fractional) cointegration in the bivariate case. For the multivariate case, there are several versions of cointegration, and the version given in Robinson and Yajima (2002) has received much attention. In this definition, a time series vector is partitioned into several sub-vectors, and the elements in each sub-vector have the same integration order. Furthermore, this time series vector is said to be cointegrated if there exists a cointegration in any of the sub-vectors. Under such a circumstance, testing for the equality of integration orders constitutes an important problem. However, for multivariate fractionally integrated series, most tests focus on stationary and invertible series and become invalid under the presence of cointegration. Hualde (2013) overcomes these difficulties with a residual-based test for a bivariate time series. For the multivariate case, one possible extension of this test involves testing for an array of bivariate series, which becomes computationally challenging as the dimension of the time series increases. In this paper, a one-step residual-based test is proposed to deal with the multivariate case that overcomes the computational issue. Under certain regularity conditions, the test statistic has an asymptotic standard normal distribution under the null hypothesis of equal integration orders and diverges to infinity under the alternative. As reported in a Monte Carlo experiment, the proposed test possesses satisfactory sizes and powers. View Full-Text
Keywords: asymptotic normal; fractional cointegration; Monte Carlo experiment; residual-based test asymptotic normal; fractional cointegration; Monte Carlo experiment; residual-based test
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, M.; Chan, N.H. Testing for the Equality of Integration Orders of Multiple Series. Econometrics 2016, 4, 49.

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