Semiparametric Independence Tests Between Two Infinite-order Cointegrated Series
Essays in Honor of Joon Y. Park: Econometric Theory
ISBN: 978-1-83753-209-4, eISBN: 978-1-83753-208-7
Publication date: 24 April 2023
Abstract
The authors propose a semiparametric approach for testing independence between two infinite-order cointegrated vector autoregressive series (IVAR(∞)). The procedures considered can be viewed as extensions of classical methods proposed by Haugh (1976, JASA) and Hong (1996b, Biometrika) for testing independence between stationary univariate time series. The tests are based on the residuals of long autoregressions, hence allowing for computational simplicity, weak assumptions on the form of the underlying process, and a direct interpretation of the results in terms of innovations (or shocks). The test statistics are standardized versions of the sum of weighted squares of residual cross-correlation matrices. The weights depend on a kernel function and a truncation parameter. Multivariate portmanteau statistics can be viewed as a special case of our procedure based on the truncated uniform kernel. The asymptotic distributions of the test statistics under the null hypothesis are derived, and consistency is established against fixed alternatives of serial cross-correlation of unknown form. A simulation study is presented which indicates that the proposed tests have good size and power properties in finite samples.
Keywords
Acknowledgements
Acknowledgments
The authors thank Yoosoon Chang, Kilani Ghoudi, Ian McLeod, Abderrahim Taamouti, and an anonymous referee for several useful comments. Earlier versions of this chapter were presented at the Statistical Society of Canada annual meeting and the University of Western Ontario (Department of Statistical and Actuarial Sciences). This work was supported by the William Dow Chair in Political Economy (McGill University), the Bank of Canada (Research Fellowship), the Toulouse School of Economics (Pierre-de-Fermat Chair of excellence), the Universitad Carlos III de Madrid (Banco Santander de Madrid Chair of excellence), a Guggenheim Fellowship, a Konrad-Adenauer Fellowship (Alexander-von-Humboldt Foundation, Germany), the Canadian Network of Centres of Excellence [program on Mathematics of Information Technology and Complex Systems (MITACS)], the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, and the Fonds de recherche sur la société et la culture (Québec).
Citation
Bouhaddioui, C., Dufour, J.-M. and Takano, M. (2023), "Semiparametric Independence Tests Between Two Infinite-order Cointegrated Series", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Theory (Advances in Econometrics, Vol. 45A), Emerald Publishing Limited, Leeds, pp. 263-294. https://doi.org/10.1108/S0731-90532023000045A009
Publisher
:Emerald Publishing Limited
Copyright © 2023 Chafik Bouhaddioui, Jean-Marie Dufour and Masaya Takano