Climatic Change

, Volume 101, Issue 3–4, pp 395–405 | Cite as

Does temperature contain a stochastic trend? Evaluating conflicting statistical results

  • Robert K. Kaufmann
  • Heikki Kauppi
  • James H. Stock


We evaluate the claim by Gay et al. (Clim Change 94:333–349, 2009) that “surface temperature can be better described as a trend stationary process with a one-time permanent shock” than efforts by Kaufmann et al. (Clim Change 77:249–278, 2006) to model surface temperature as a time series that contains a stochastic trend that is imparted by the time series for radiative forcing. We test this claim by comparing the in-sample forecast generated by the trend stationary model with a one-time permanent shock to the in-sample forecast generated by a cointegration/error correction model that is assumed to be stable over the 1870–2000 sample period. Results indicate that the in-sample forecast generated by the cointegration/error correction model is more accurate than the in-sample forecast generated by the trend stationary model with a one-time permanent shock. Furthermore, Monte Carlo simulations of the cointegration/error correction model generate time series for temperature that are consistent with the trend-stationary-with-a-break result generated by Gay et al. (Clim Change 94:333–349, 2009), while the time series for radiative forcing cannot be modeled as trend stationary with a one-time shock. Based on these results, we argue that modeling surface temperature as a time series that shares a stochastic trend with radiative forcing offers the possibility of greater insights regarding the potential causes of climate change and efforts to slow its progression.


Southern Hemisphere Unit Root Temperature Time Series Stochastic Trend Hemisphere Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bloomfield P, Nychka D (1992) Climate spectra and detecting climate change. Clim Change 21:275–287CrossRefGoogle Scholar
  2. Christiano, LJ (1992) Searching for a break in GNP. J Bus Econ Stat 10(3):237–250CrossRefGoogle Scholar
  3. Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74:427–431CrossRefGoogle Scholar
  4. Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 13:253–263CrossRefGoogle Scholar
  5. Gay C, Estrada F, Sanchez A (2009) Global and hemispheric temperature revisited. Clim Change 94:333–349. doi: 10.1007/s10584-008-9524-8 CrossRefGoogle Scholar
  6. Jones PD, Parker DE, Osborn TJ, Briffa KR (2006) Global and hemispheric temperature anomalies—land and marine instrumental records. In: Trends: a compendium of data on global change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak RidgeGoogle Scholar
  7. Kaufmann RK, Stern DI (1997) Evidence for human influence on climate from hemispheric temperature relations. Nature 388:39–44CrossRefGoogle Scholar
  8. Kaufmann RK, Stern DI (2002) Cointegration analysis of hemispheric temperature relations. J Geophys Res 107(d2):ACL8-1–10. doi: 10.1029/2000JD000174 CrossRefGoogle Scholar
  9. Kaufmann RK, Kauppi H, Stock JH (2006) Emissions, concentrations, & temperature: a time series analysis. Clim Change 77:249–278CrossRefGoogle Scholar
  10. Kiehl JT, Briegleb BP (1993) The relative roles of sulfate aerosols and greenhouse gases in climate forcing. Science 260:311–314CrossRefGoogle Scholar
  11. Kim D, Perron P (2007) Unit root tests allowing for a break in the trend function under the null and alternative hypothesis. Unpublished manuscript, Department of Economics, Boston UniversityGoogle Scholar
  12. Kim K, Schmidt P (1990) Some evidence on the accuracy of Phillips–Perron tests using alternative estimates of nuisance parameters. Econ Lett 34:345–350CrossRefGoogle Scholar
  13. Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root. J Econom 54:159–178CrossRefGoogle Scholar
  14. Lehmann EL (1975) Nonparametrics, statistical methods based on ranks. McGraw-Hill, San FranciscoGoogle Scholar
  15. Mills TC (2009) How robust is the long-run relationship between temperature and radiative forcing? Clim Change 94:351–361. doi: 10.1007/S10584-008-9525-7 CrossRefGoogle Scholar
  16. Perron P (1997) Further evidence on breaking trend functions in macroeconomic variables. J Econom 80(2):355–385CrossRefGoogle Scholar
  17. Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75:335–346CrossRefGoogle Scholar
  18. Schmidt P, Phillips PCB (1992) LM tests for a unit root in the presence of deterministic trends. Oxf Bull Econ Stat 54:257–287Google Scholar
  19. Schwert GW (1989) Tests for unit roots: a Monte Carlo investigation. J Bus Econ Stat 7:147–159CrossRefGoogle Scholar
  20. Stern DI (2005) A three layer atmosphere–ocean time series model of global climate change. Renselear Polytechnic Institute (Mimeo)Google Scholar
  21. Stern DI, Kaufmann RK (2000) Detecting a global warming signal in hemispheric temperature series: a structural time series analysis. Clim Change 47:411–438CrossRefGoogle Scholar
  22. Wigley TML, Smith RL, Santer BD (1998) Anthropogenic influence on the autocorrelation structure of hemispheric-mean temperatures. Science 282:1676–1679CrossRefGoogle Scholar
  23. Woodward WA, Gray HL (1993) Global warming and the problem of testing for trend in time series data. J Clim 6:953–962CrossRefGoogle Scholar
  24. Woodward WA, Gray HL (1995) Selecting a model for detecting the presence of a trend. J Clim 8:1929–1937CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Robert K. Kaufmann
    • 1
  • Heikki Kauppi
    • 2
  • James H. Stock
    • 3
  1. 1.Center for Energy & Environmental StudiesBoston UniversityBostonUSA
  2. 2.Department of EconomicsUniversity of HelsinkiArkadiankatu 7Finland
  3. 3.Department of EconomicsHarvard UniversityCambridgeUSA

Personalised recommendations