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Cotrending: Testing for common deterministic trends in varying means model

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  • Düker, Marie-Christine
  • Pipiras, Vladas
  • Sundararajan, Raanju

Abstract

In a varying means model, the temporary evolution of a p-vector system is determined by p deterministic nonparametric functions superimposed by error terms, possibly dependent cross sectionally. The basic interest is in linear combinations across the p dimensions that make the deterministic functions constant over time. The number of such linearly independent linear combinations is referred to as a cotrending dimension, and their spanned space as a cotrending space. This work puts forward a framework to test statistically for cotrending dimension and space. Connections to principal component analysis and cointegration are also considered. Finally, a simulation study to assess the finite-sample performance of the proposed tests, and applications to several real data sets are also provided.

Suggested Citation

  • Düker, Marie-Christine & Pipiras, Vladas & Sundararajan, Raanju, 2022. "Cotrending: Testing for common deterministic trends in varying means model," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jmvana:v:187:y:2022:i:c:s0047259x21001032
    DOI: 10.1016/j.jmva.2021.104825
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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    3. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    4. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(2), pages 151-175, April.
    5. Raanju Ragavendar Sundararajan & Mohsen Pourahmadi, 2018. "Stationary subspace analysis of nonstationary processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(3), pages 338-355, May.
    6. Cardinali, Alessandro & Nason, Guy P., 2013. "Costationarity of Locally Stationary Time Series Using costat," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i01).
    7. Darryl Holden & Roger Perman, 1994. "Unit Roots and Cointegration for the Economist," Palgrave Macmillan Books, in: B. Bhaskara Rao (ed.), Cointegration, chapter 3, pages 47-112, Palgrave Macmillan.
    8. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.
    9. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    10. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    12. Camba-Méndez, Gonzalo & Kapetanios, George, 2001. "Testing the rank of the Hankel matrix: a statistical approach," Working Paper Series 45, European Central Bank.
    13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    14. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    15. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    16. Maddala,G. S. & Kim,In-Moo, 1999. "Unit Roots, Cointegration, and Structural Change," Cambridge Books, Cambridge University Press, number 9780521587822, October.
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