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Multivariate trend comparisons between autocorrelated climate series with general trend regressors

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  • Ross McKitrick

    ()
    (Department of Economics and Finance, University of Guelph)

  • Timothy Vogelsang

    ()
    (Department of Economics, Michigan State University)

Abstract

Inference regarding trends in climatic data series, including comparisons across different data sets as well as univariate trend significance tests, is complicated by the presence of serial correlation and step-changes in the mean. We review recent developments in the estimation of heteroskedasticity and autocorrelation robust (HAC) covariance estimators as they have been applied to linear trend inference, with focus on the Vogelsang-Franses (2005) nonparametric approach, which provides a unified framework for trend covariance estimation robust to unknown forms of autocorrelation up to but not including unit roots, making it especially useful for climatic data applications. We extend the Vogelsang-Franses approach to allow general deterministic regressors including the case where a step-change in the mean occurs at a known date. Additional regressors change the critical values of the Vogelsang-Franses statistic. We derive an asymptotic approximation that can be used to simulate critical values. We also outline a simple bootstrap procedure that generates valid critical values and p-values. The motivation for extending the Vogelsang-Franses approach is an application that compares climate model generated and observational global temperature data in the tropical lower- and mid-troposphere from 1958 to 2010. Inclusion of a mean shift regressor to capture the Pacific Climate Shift of 1977 causes apparently significant observed trends to become statistically insignificant, and rejection of the equivalence between model generated and observed data trends occurs for much smaller significance levels (i.e. is more strongly rejected).

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Bibliographic Info

Paper provided by University of Guelph, Department of Economics and Finance in its series Working Papers with number 1109.

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Length: 34 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:gue:guelph:2011-09.

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Keywords: Autocorrelation; trend estimation; HAC variance matrix; global warming; model comparisons;

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References

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  1. Gonçalves, Sílvia & Vogelsang, Timothy J., 2011. "Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap," Econometric Theory, Cambridge University Press, vol. 27(04), pages 745-791, August.
  2. Vogelsang, Timothy J. & Franses, Philip Hans, 2005. "Testing for common deterministic trend slopes," Journal of Econometrics, Elsevier, vol. 126(1), pages 1-24, May.
  3. Fomby, Tom & Vogelsang, Tim, 2000. "The Application of Size Robust Trend Analysis to Global Warming Temperature Series," Working Papers 00-08, Cornell University, Center for Analytic Economics.
  4. Nicholas M. Kiefer & Timothy J. Vogelsang, 2002. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation," Econometrica, Econometric Society, vol. 70(5), pages 2093-2095, September.
  5. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  6. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
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