Accessible Unlicensed Requires Authentication Published online by De Gruyter October 15, 2021

Recovering cointegration via wavelets in the presence of non-linear patterns

Jorge Martínez Compains, Ignacio Rodríguez Carreño ORCID logo, Ramazan Gençay, Tommaso Trani ORCID logo and Daniel Ramos Vilardell

Abstract

Johansen’s Cointegration Test (JCT) performs remarkably well in finding stable bivariate cointegration relationships. Nonetheless, the JCT is not necessarily designed to detect such relationships in presence of non-linear patterns such as structural breaks or cycles that fall in the low frequency portion of the spectrum. Seasonal adjustment procedures might not detect such non-linear patterns, and thus, we expose the difficulty in identifying cointegrating relations under the traditional use of JCT. Within several Monte Carlo experiments, we show that wavelets can empower more the JCT framework than the traditional seasonal adjustment methodologies, allowing for identification of hidden cointegrating relationships. Moreover, we confirm these results using seasonally adjusted time series as US consumption and income, gross national product (GNP) and money supply M1 and GNP and M2.

JEL Classification: C01; C12; C22

Corresponding author: Jorge Martínez Compains, Department of Economics, Simon Fraser University, Vancouver, Canada, E-mail:

Funding source: Ministerio de Economía, Industria y Competitividad

Award Identifier / Grant number: ECO 2015-68815-P

Award Identifier / Grant number: ECO 2017-83183-R

Acknowledgments

The authors are grateful to the Editor and an anonymous referee for his comments. They thank seminar and conference participants at the Simon Fraser University and İstanbul Bilgi University. Ignacio Rodríguez Carreno thanks the Department of Economics of Simon Fraser University, where part of this research was conducted, for their hospitality. Finally, special thanks to our friend Ramo, in memoriam.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Ignacio Rodriguez Carreño also gratefully acknowledges the financial support received from the Ministerio de Economía, Industria y Competitividad (ECO 2017-83183-R). Tommaso Trani gratefully acknowledges the financial support received from the Ministerio de Economía, Industria y Competitividad (ECO 2015-68815-P).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Abeln, B., and J. Jacobs. 2015. “Seasonal Adjustment with and without Revisions: A Comparison of X-13ARIMA-SEATS and CAMPLET.” In CAMA Working Paper No. 25/2015. Available at SSRN: https://doi.org/10.2139/ssrn.2635289. Search in Google Scholar

Banerjee, A., and G. Urga. 2005. “Modelling Structural Breaks, Long Memory and Stock Market Volatility: An Overview.” Journal of Econometrics 129: 1–34. https://doi.org/10.1016/j.jeconom.2004.09.001. Search in Google Scholar

Berger, T., and R. Gençay. 2018. “Improving Daily Value-At-Risk Forecasts: The Relevance of Short-Run Volatility for Regulatory Quality Assessment.” Journal of Economic Dynamics and Control 92: 30–46. https://doi.org/10.1016/j.jedc.2018.03.016. Search in Google Scholar

Bergmeir, C., R. J. Hyndman, and J. M. Benítez. 2016. “Bagging Exponential Smoothing Methods Using STL Decomposition and Box–Cox Transformation.” International Journal of Forecasting 32 (2): 303–12. https://doi.org/10.1016/j.ijforecast.2015.07.002. Search in Google Scholar

Eiurridge, P., and K. F. Wallis. 1990. “Seasonal Adjustment and Kalman Filtering: Extension to Periodic Variances.” Journal of Forecasting 9 (2): 109–18. https://doi.org/10.1002/for.3980090204. Search in Google Scholar

Engle, R. F., and C. W. J. Granger, 1987. “Co-Integration and Error Correction: Representation, Estimation, and Testing,” Econometrica 55 (2): 251–76. https://doi.org/10.2307/1913236. Search in Google Scholar

Eroğlu, B., and B. Soybilgen. 2018. “On the Performance of Wavelet Based Unit Root Tests.” JRFM 11 (3): 47. Search in Google Scholar

Fan, Y., and R. Gençay. 2010. “Unit Root Tests with Wavelets.” Econometric Theory 26 (05): 1305–31. https://doi.org/10.1017/s0266466609990594. Search in Google Scholar

Ghysels, E., and P. Perron. 1993. “The Effect of Seasonal Adjustment Filters on Tests for a Unit Root.” Journal of Econometrics 55 (1–2): 57–98. https://doi.org/10.1016/0304-4076(93)90004-o. Search in Google Scholar

Granger, C. W. J. 1966. “The Typical Spectral Shape of an Economic Variable.” Econometrica 34 (1): 150–61. https://doi.org/10.2307/1909859. Search in Google Scholar

Hamilton, J. D. 1989. “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica 57 (2): 357–84. https://doi.org/10.2307/1912559. Search in Google Scholar

Hassani, H., A. Webster, E. S. Silva, and S. Heravi. 2015. “Forecasting U.S. Tourist Arrivals Using Optimal Singular Spectrum Analysis.” Tourism Management 46: 322–35. https://doi.org/10.1016/j.tourman.2014.07.004. Search in Google Scholar

Johansen, S. 1991. “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models.” Econometrica 59 (6): 1551–80. https://doi.org/10.2307/2938278. Search in Google Scholar

Kobbi, I., and F. B. Gabsi. 2020. “Nonlinearities in Central Bank of Tunisia’s Reaction Function: Pre-and Post Revolution Analysis.” International Economic Journal 34: 169–83. https://doi.org/10.1080/10168737.2019.1704821. Search in Google Scholar

Lengwiler, Y. 2017. X-13 Toolbox for Matlab, Version 1.32. Mathworks File Exchange. Also available at: http://ch.mathworks.com/matlabcentral/fileexchange/49120-x-13-toolbox-for-seasonal-filtering. Search in Google Scholar

Li, Y., and G. Shukur. 2011. “Testing for Unit Roots in Panel Data Using a Wavelet Ratio Method.” Comput Econ 41 (1): 59–69. Search in Google Scholar

Mallat, S. G. 1989. “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 11 (7): 674–93. https://doi.org/10.1109/34.192463. Search in Google Scholar

Percival, D., and A. Walden. 2000. Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press. Search in Google Scholar

Ramsey, J. B. 2002. “Wavelets in Economics and Finance: Past and Future.” Studies in Nonlinear Dynamics & Econometrics 3: 1–29. https://doi.org/10.2202/1558-3708.1090. Search in Google Scholar

Sims, C. A. 1974. “Seasonality in Regression.” Journal of the American Statistical Association 69 (347): 618–26. https://doi.org/10.1080/01621459.1974.10480178. Search in Google Scholar

Trokic, M. 2016. “Wavelet Energy Ratio Unit Root Tests.” Econometric Reviews 1–19. Search in Google Scholar

Uddin, G. S., R. Gençay, S. Stelios Bekiros, and M. Sahamkhadam. 2019. “Enhancing the Predictability of Crude Oil Markets with Hybrid Wavelet Approaches.” Economics Letters 182: 50–4. https://doi.org/10.1016/j.econlet.2019.05.041. Search in Google Scholar

Wong, H., I. Wai-Cheung, X. Zhongjie, and L. Xueli. 2003. “Modelling and Forecasting by Wavelets, and the Application to Exchange Rates.” Journal of Applied Statistics 30 (5): 537–53. https://doi.org/10.1080/0266476032000053664. Search in Google Scholar

Xue, Y., R. Gençay, and S. Fagan. 2014. “Jump Detection with Wavelets for High-Frequency Financial Time Series.” Quantitative Finance 14 (8): 1427–44. https://doi.org/10.1080/14697688.2013.830320. Search in Google Scholar

Zhang, K., R. Gençay, and M. E. Yazgan. 2017. “Application of Wavelet Decomposition in Time-Series Forecasting.” Economics Letters 158: 41–6. https://doi.org/10.1016/j.econlet.2017.06.010. Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2018-0120).

Received: 2018-12-12
Accepted: 2021-09-21
Published Online: 2021-10-15

© 2021 Walter de Gruyter GmbH, Berlin/Boston