Detecting a Global Warming Signal in Hemispheric Temperature Series: AStructural Time Series Analysis
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Abstract
Non-stationary time series such as global andhemispheric temperatures, greenhouse gasconcentrations, solar irradiance, and anthropogenicsulfate aerosols, may contain stochastic trends (thesimplest stochastic trend is a random walk) which, dueto their unique patterns, can act as a signal of theinfluence of other variables on the series inquestion. Two or more series may share a commonstochastic trend, which indicates that either oneseries causes the behavior of the other or that thereis a common driving variable. Recent developments ineconometrics allow analysts to detect and classifysuch trends and analyze relationships among seriesthat contain stochastic trends. We apply someunivariate autoregression based tests to evaluate thepresence of stochastic trends in several time seriesfor temperature and radiative forcing. The temperatureand radiative forcing series are found to be ofdifferent orders of integration which would cast doubton the anthropogenic global warming hypothesis.However, these tests can suffer from size distortionswhen applied to noisy series such as hemispherictemperatures. We, therefore, use multivariatestructural time series techniques to decomposeNorthern and Southern Hemisphere temperatures intostochastic trends and autoregressive noise processes. These results show that there are two independentstochastic trends in the data. We investigate thepossible origins of these trends using a regressionmethod. Radiative forcing due to greenhouse gases andsolar irradiance can largely explain the common trend.The second trend, which represents the non-scalarnon-stationary differences between the hemispheres,reflects radiative forcing due to tropospheric sulfateaerosols. We find similar results when we use the sametechniques to analyze temperature data generated bythe Hadley Centre GCM SUL experiment.
Keywords
Global Warming Solar Irradiance Stochastic Trend Series Technique Hemisphere TemperaturePreview
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References
- Akaike, H.: 1973, 'Information Theory and an Extension of the Maximum Likelihood Principle', in Petrov, B. N. and Csaki, F. (eds.), 2nd International Symposium on Information Theory, Akademini Kiado, Budapest, pp. 267-281.Google Scholar
- Andrews, D. W. K.: 1991, 'Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation', Econometrica 59, 817-858.Google Scholar
- A.S.L. and Associates: 1997, Sulfur Emissions by Country and Year, Report No. DE96014790, U.S. Department of Energy, Washington D.C.Google Scholar
- Battle, M., Bender, M., Sowers, T., Tans, P. P., Butler, J. H., Elkins, J. W., Ellis, J. T., Conway, T., Zhang, N., Lang, P., and Clarke, A. D.: 1996, 'Atmospheric Gas Concentrations over the Past Century Measured in Air from Firn at the South Pole', Nature 383, 231-235.Google Scholar
- Berndt, E., Hall, B., Hall, R. E., and Hausman, J. A.: 1974, 'Estimation and Inference in Non-Linear Structural Models', Ann. Econ. Soc. Measure. 55, 653-665.Google Scholar
- Chernoff, H.: 1954, 'On the Distribution of the Likelihood Ratio', Ann. Math. Stat. 25, 573-578.Google Scholar
- Cunnold, D., Fraser, P., Weiss, R., Prinn, R., Simmonds, P., Miller, B., Alyea, F., and Crawford, A.: 1994, 'Global Trends and Annual Releases of CCl3F and CCl2F2 Estimated from ALE/GAGE and Other Measurements from July 1978 to June 1991', J. Geophys. Res. 99 (D1), 1107-1126.Google Scholar
- De Jong, P.: 1988, 'The Likelihood for a State Space Model', Biometrika 75, 165-169.Google Scholar
- De Jong, P.: 1991a, 'Stable Algorithms for the State Space Model', J. Time Ser. Anal. 12 (2), 143-157.Google Scholar
- De Jong, P.: 1991b, 'The Diffuse Kalman Filter', Ann. Stat. 19, 1073-1083.Google Scholar
- Dickey, D. A. and Fuller, W. A.: 1979, 'Distribution of the Estimators for Autoregressive Time Series with a Unit Root', J. Amer. Stat. Assoc. 74, 427-431.Google Scholar
- Dickey, D. A. and Fuller, W. A.: 1981, 'Likelihood Ratio Statistics for Autoregressive Processes', Econometrica 49, 1057-1072.Google Scholar
- Dlugokenchy, E. J., Lang, P. M., Masarie, K. A., and Steele, L. P.: 1994, 'Global CH4 Record from the NOAA/CMDL Air Sampling Network', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. S. (eds.), Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 262-266.Google Scholar
- Enders, W.: 1995, Applied Econometric Time Series, John Wiley, New York.Google Scholar
- Engle, R. E. and Granger, C. W. J.: 1987, 'Cointegration and Error-Correction: Representation, Estimation, and Testing', Econometrica 55, 251-276.Google Scholar
- Etheridge, D.M., Pearman, G. I., and Fraser, P. J.: 1994, 'Historical CH4 Record from the “DE08” Ice Core at Law Dome', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. S. (eds.), Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 256-260.Google Scholar
- Etheridge, D. M., Steele, L. P., Langenfelds, R. L., Francey, R. J., Barnola, J.-M., and Morgan, V. I.: 1996, 'Natural and Anthropogenic Changes in Atmospheric CO2 over the Last 1000 Years from Air in Antarctic Ice and Firn', J. Geophys. Res. 101, 4115-4128.Google Scholar
- Fletcher, R. and Powell, M. J. D.: 1963, 'A Rapidly Convergent Descent Method for Minimization', Computer J. 6, 163-168.Google Scholar
- Folland, C. K., Karl, T. R., Nicholls, N., Nyenzi, B. S., Parker, D. E., and Vinnikov, K. Y.: 1992, 'Observed Climate Variability and Change', in Houghton, J. T., Callander, B. A., and Varney, S. K. (eds.), Climate Change 1992: The Supplementary Report to the IPCC Scientific Assessment, Cambridge University Press, Cambridge, pp. 139-170.Google Scholar
- Granger C. W. J. and Newbold, P.: 1974, 'Spurious Regressions in Econometrics', J. Econometrics 35, 143-159.Google Scholar
- Haldrup, N.: 1997, A Review of the Econometric Analysis of I(2) Variables, Working Paper No. 1997-12, Centre for Non-linear Modelling in Economics, University of Aarhus, Aarhus, Denmark.Google Scholar
- Hamilton, J. D.: 1994, Time Series Analysis, Princeton University Press, Princeton, NJ.Google Scholar
- Hansen, H. and Juselius, K.: 1995, CATS in RATS: Cointegration Analysis of Time Series, Estima, Evanston IL.Google Scholar
- Harman, H. H.: 1976, Modern Factor Analysis, University of Chicago Press, Chicago, IL.Google Scholar
- Harvey, A. C.: 1989, Forecasting, Structural Time Series Models, and the Kalman Filter, Cambridge University Press, Cambridge.Google Scholar
- Harvey, A. C.: 1993, Time Series Models, 2nd edn., Harvester Wheatsheaf, London.Google Scholar
- Johansen, S.: 1988, 'Statistical Analysis of Cointegration Vectors', J. Econ. Dyn. Control 12, 231-254.Google Scholar
- Jones, P. D., Wigley, T. M. L., and Biffa, K. R.: 1994, 'Global and Hemispheric Temperature Anomalies-Land and Marine Instrumental Records', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. S. (eds.), Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 603-608.Google Scholar
- Kattenberg, A., Giorgi, F., Grassl, H., Meehl, G. A., Mitchell, J. F. B., Stouffer, R. J., Tokioka, T., Weaver, A. J., and Wigley, T. M. L.: 1996, 'Climate Models-Projections of Future Climate', in Houghton, J. T., Meira Filho, L. G., Callander, B. A., Harris, N., Kattenberg, A., and Maskell, K. (eds.), Climate Change 1995: The Science of Climate Change, Cambridge University Press, Cambridge, pp. 285-357.Google Scholar
- Kaufmann, R. K. and Stern, D. I.: 1997, 'Evidence for Human Influence on Climate from Hemispheric Temperature Relations', Nature 388, 39-44.Google Scholar
- Keeling, C. D. and Whorf, T. P.: 1994, 'Atmospheric CO2 Records from Sites in the SIO Air Sampling Network', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., Stoss, F. S. (eds.) Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 16-26.Google Scholar
- Kiehl, J. T. and Briegleb, B. P.: 1993, 'The Relative Roles of Sulfate Aerosols and Greenhouse Gases in Climate Forcing', Science 260, 311-314.Google Scholar
- Kim, K. and Schmidt, P.: 1990, 'Some Evidence on the Accuracy of Phillips-Perron Tests Using Alternative Estimates of Nuisance Parameters', Econ. Lett. 34, 345-350.Google Scholar
- Kitamura, Y.: 1995, 'Estimation of Cointegrated Systems with I(2) Processes', Econometric Theory 11, 1-24.Google Scholar
- Kuo, C., Lindberg, C., and Thomson D. J.: 1990, 'Coherence Established between Atmospheric Carbon Dioxide and Global Temperature', Nature 343, 709-714.Google Scholar
- Kwiatowski, D., Phillips, P. C. B., Schmidt, P., and 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. Econometrics 54, 159-178.Google Scholar
- Lean, J., Beer, J., and Bradley, R.: 1995, 'Reconstruction of Solar Irradiance since 1610: Implications for Climate Change', Geophys. Res. Lett. 22, 3195-3198.Google Scholar
- Ljung, G. M. and Box, G. E. P.: 1978, 'On a Measure of Lack of Fit in Time Series Models', Biometrika 65, 297-303.Google Scholar
- Machida, T., Nakazawa, T., Fujii, Y., Aoki, S., and Watanabe, O.: 1995, 'Increase in the Atmospheric Nitrous Oxide Concentration during the Last 250 Years', Geophys. Res. Lett. 22, 2921-2924.Google Scholar
- Mitchell, J. F. B., Johns, T. C., Gregory, J. M., and Tett, S. F. B.: 1995, Climate Response to Increasing Levels of Greenhouse Gases and Sulfate Aerosols, Nature 376, 501-504.Google Scholar
- Newey, W. K. and West, K. D.: 1987: 'A Simple Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix', Econometrica 55, 1029-1054.Google Scholar
- Pantula, S.: 1991, 'Asymptotic Distributions of Unit-Root Tests when the Process is Nearly Stationary', J. Busin. Econ. Stat. 9, 63-71.Google Scholar
- Phillips, P. C. B.: 1991, 'Optimal Inference in Cointegrated Systems', Econometrica 59, 283-306.Google Scholar
- Phillips, P. C. B. and Ouliaris, S.: 1990, 'Asymptotic Properties of Residual Based Test for Cointegration', Econometrica 58, 190.Google Scholar
- Phillips, P. C. B. and Perron, P.: 1988, 'Testing for a Unit Root in Time Series Regression', Biometrika 75, 335-346.Google Scholar
- Prather, M., McElroy, M., Wofsy, S., Russel, G., and Rind, D.: 1987, 'Chemistry of the Global Troposphere: Fluorocarbons as Tracers of Air Motion', J. Geophys. Res. 92D, 6579-6613.Google Scholar
- Prinn, R. G., Cunnold, D., Fraser, P., Weiss, R., Simmonds, P., Alyea, F., Steele, L. P., and Hartley, D.: 1997, CDIAC World Data Center Dataset No. DB-1001/R3 (anonymous ftp from cdiac.esd@ornl.gov).Google Scholar
- Prinn, R. G., Cunnold, D., Rasmussen, R., Simmonds, P., Alyea, F., Crawford, A., Fraser, P., and Rosen, R.: 1990, 'Atmospheric Emissions and Trends of Nitrous Oxide Deduced from Ten Years of ALE/GAGE Data', J. Geophys. Res. 95, 18369-18385.Google Scholar
- Richards, G. R.: 1993, 'Change in Global Temperature: a Statistical Analysis', J. Climate 6, 546-559.Google Scholar
- Sato, M., Hansen, J. E., McCormick, M. P., and Pollack, J. B.: 1993, 'Stratospheric Aerosol Optical Depths, 1850-1990', J. Geophys. Res. 98, 22987-22994.Google Scholar
- Schmidt, P. and Phillips, P. C. B.: 1992, 'LM Tests for a Unit Root in the Presence of Deterministic Trends', Oxford Bull. Econ. Stat. 54, 257-287.Google Scholar
- Schönwiese, C.-D.: 1994, 'Analysis and Prediction of Global Climate Temperature Change Based on Multiforced Observational Statistics', Environ. Pollut. 83, 149-154.Google Scholar
- Schweppe, F.: 1965, 'Evaluation of Likelihood Functions for Gaussian Signals', IEEE Trans. Information Theory 11, 61-70.Google Scholar
- Schwert, G. W.: 1989, 'Tests for Unit Roots: a Monte Carlo Investigation', J. Busin. Econ. Stat. 7, 147-159.Google Scholar
- Shine, K. P. R. G., Derwent, D. J., Wuebbles, D. J., and Mocrette, J. J.: 1991, 'Radiative Forcing of Climate', in Houghton, J. T., Jenkins, G. J., and Ephramus, J. J. (eds.), Climate Change: The IPCC Scientific Assessment, Cambridge University Press, Cambridge, pp. 47-68.Google Scholar
- Stern, D. I. and Kaufmann, R. K.: 1996, Estimates of Global Anthropogenic Sulfate Emissions 1860-1993, CEES Working Papers 9601, Center for Energy and Environmental Studies, Boston University (available on WWWat: http://cres.anu.edu.au/ dstern/mirror.html).Google Scholar
- Stern, D. I. and Kaufmann, R. K: 1999, 'Econometric Analysis of Global Climate Change', Environ. Model. Software 14, 597-605.Google Scholar
- Stock, J. H. and Watson, M. W.: 1993, 'A Simple Estimator of the Cointegrating Vectors in Higher Order Integrated Systems', Econometrica 61, 783-820.Google Scholar
- Thomson, D. J.: 1995, 'The Seasons, Global Temperature, and Precession', Science 268, 59-68.Google Scholar
- Thomson, D. J.: 1997, 'Dependence of Global Temperatures on Atmospheric CO2 and Solar Irradiance', Proc. Natl. Acad. Sci. 94, 8370-8377.Google Scholar
- Tol, R. S. J.: 1994, 'Greenhouse Statistics-Time Series Analysis: Part II', Theor. Appl. Climatol. 49, 91-102.Google Scholar
- Tol, R. S. J. and de Vos, A. F.: 1993, 'Greenhouse Statistics-Time Series Analysis', Theor. Appl. Climatol. 48, 63-74.Google Scholar
- Tol, R. S. J. and de Vos, A. F.: 1998, 'A Bayesian Statistical Analysis of the Enhanced Greenhouse Effect', Clim. Change 38, 87-112.Google Scholar
- Wigley, T.M. L.: 1989, 'Possible Climate Change Due to SO2-Derived Cloud Condensation Nuclei', Nature 339, 356-367.Google Scholar
- Wigley, T.M. L. and Raper, S. C. B.: 1992, 'Implications for Climate and Sea Level of Revised IPCC Emissions Scenarios', Nature 357, 293-300.Google Scholar
- Wigley, T. M. L., Smith, R. L., and Santer, B. D.: 1998, 'Anthropogenic Influence on the Autocorrelation Structure of Hemispheric-Mean Temperatures', Science 282, 1676-1679.Google Scholar
- Woodward, W. A. and Gray, H. L.: 1993, 'Global Warming and the Problem of Testing for Trend in Time Series Data', J. Climate 6, 953-962.Google Scholar
- Woodward, W. A. and Gray, H. L.: 1995, 'Selecting a Model for Detecting the Presence of a Trend', J. Climate 8, 1929-1937.Google Scholar
- Yoo, B. S.: 1986, Multi-Cointegrated Time Series and a Generalized Error-Correction Model, University of California at San Diego Department of Economics Discussion Paper.Google Scholar