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Testing for common deterministic trend slopes

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  • Vogelsang, T.J.
  • Franses, Ph.H.B.F.

Abstract

We propose tests for hypotheses on the parameter for deterministic trends. The model framework assumes a multivarariat stucture for trend-stationary time series variables. We derive the asymptotic theory and provide some relevant critical values. Monte Carlo simulations suggest which tests are more useful in practice than others. We apply our tests to examine if monthly temperatures in the Netherlands, measured from 1706 onwards, have a trend and if these trends are the same across months. We find that the January and March temperatures have the same upward trend, that the September temperature has decreased and that the temperatures in the other months do not have a trend. Hence, only winters in the Netherlands seem to get warmer.

Suggested Citation

  • Vogelsang, T.J. & Franses, Ph.H.B.F., 2001. "Testing for common deterministic trend slopes," Econometric Institute Research Papers EI 2001-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1680
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    1. Ross McKitrick & Timothy Vogelsang, 2011. "Multivariate trend comparisons between autocorrelated climate series with general trend regressors," Working Papers 1109, University of Guelph, Department of Economics and Finance.
    2. Noriega, Antonio E. & Soria, Luis M. & Velázquez, Ramón, 2008. "International evidence on stochastic and deterministic monetary neutrality," Economic Modelling, Elsevier, vol. 25(6), pages 1261-1275, November.
    3. Pierre Perron & Eduardo Zorita & Timothy J. Vogelsang & Nasreen Nawaz, 2017. "Estimation and Inference of Linear Trend Slope Ratios With an Application to Global Temperature Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 640-667, September.
    4. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
    5. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    6. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
    7. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, February.
    8. Nuno Sobreira & Luis C. Nunes, 2016. "Tests for Multiple Breaks in the Trend with Stationary or Integrated Shocks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 394-411, June.
    9. Joseph P. Byrne & Roger Perman, 2006. "Unit Roots and Structural Breaks: A Survey of the Literature," Working Papers 2006_10, Business School - Economics, University of Glasgow.
    10. Ke-Li Xu & Jui-Chung Yang, 2015. "Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non-stationary Volatility," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 63-86, March.
    11. R. Velazquez & Noriega & A., 2004. "International evidence on monetary neutrality under broken trend stationary models," Computing in Economics and Finance 2004 282, Society for Computational Economics.
    12. Xu, Ke-Li, 2016. "Multivariate trend function testing with mixed stationary and integrated disturbances," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 38-57.
    13. Lyubchich, Vyacheslav & Gel, Yulia R., 2016. "A local factor nonparametric test for trend synchronism in multiple time series," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 91-104.
    14. Eun, Cheol S. & Lee, Jinsoo, 2010. "Mean-variance convergence around the world," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 856-870, April.
    15. Erhua Zhang & Xiaojun Song & Jilin Wu, 2022. "A non‐parametric test for multi‐variate trend functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 856-871, November.

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