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Estimation and Inference of Linear Trend Slope Ratios With an Application to Global Temperature Data

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  • Pierre Perron
  • Eduardo Zorita
  • Timothy J. Vogelsang
  • Nasreen Nawaz

Abstract

We focus on estimation and inference of the ratio of trend slopes between two time series where the trending behavior of each series can be well approximated by a simple linear time trend. Our methodological results are motivated by a recent empirical climate literature that seeks to estimate and test hypotheses about the relative rate of warming in the lower-troposphere relative to surface warming - the so-called amplification ratio. We analyze the statistical properties of several estimators and test statistics that are configured to allow serial correlation in the data. The relative merits of the estimators and test statistics depend on the magnitude of the trend slopes relative to the noise in the data. Based on asymptotic theory and finite sample evidence, we make specific and concrete recommendations for practitioners. We apply the recommended estimator and confidence intervals to temperature data from the 1979-2014 period. We find that amplification ratios typically associated with climate models are rejected by the observed temperature data confirming and extending the empirical findings of Klotzbach et al (2009, 2010). Allowing for a structural change at the end of 1998 to account for the so-called "hiatus" in warming gives results similar to Klotzbach et al (2009, 2010).
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  • 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.
    • Handle: RePEc:bla:jtsera:v:38:y:2017:i:5:p:640-667
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    File URL: http://hdl.handle.net/10.1111/jtsa.12209
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    1. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    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. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    4. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    5. Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
    6. Fagerberg, Jan, 1994. "Technology and International Differences in Growth Rates," Journal of Economic Literature, American Economic Association, vol. 32(3), pages 1147-1175, September.
    7. 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.
    8. Ross R. McKitrick & Timothy J. Vogelsang, 2014. "HAC robust trend comparisons among climate series with possible level shifts," Environmetrics, John Wiley & Sons, Ltd., vol. 25(7), pages 528-547, November.
    9. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(4), pages 995-1029, August.
    10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    11. Paul Evans, 1997. "How Fast Do Economies Converge?," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 219-225, May.
    12. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    13. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, May.
    14. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    15. Francisco Estrada & Pierre Perron & Benjamin Martinez-Lopez, 2013. "Statistically-derived contributions of diverse human influences to 20th century temperature changes," Boston University - Department of Economics - Working Papers Series 2013-017, Boston University - Department of Economics.
    16. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    17. Yixiao Sun, 2014. "Fixed‐Smoothing Asymptotics in a Two‐Step Generalized Method of Moments Framework," Econometrica, Econometric Society, vol. 82, pages 2327-2370, November.
    18. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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