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Change points and temporal dependence in reconstructions of annual temperature: did Europe experience a little ice age? (English) Zbl 1303.86005

Summary: We analyze the timing and extent of Northern European temperature falls during the Little Ice Age, using standard temperature reconstructions. However, we can find little evidence of temporal dependence or structural breaks in European weather before the twentieth century. Instead, European weather between the fifteenth and nineteenth centuries resembles uncorrelated draws from a distribution with a constant mean (although there are occasional decades of markedly lower summer temperature) and variance, with the same behavior holding more tentatively back to the twelfth century. Our results suggest that observed conditions during the Little Ice Age in Northern Europe are consistent with random climate variability. The existing consensus about apparent cold conditions may stem in part from a Slutsky effect, where smoothing data gives the spurious appearance of irregular oscillations when the underlying time series is white noise.

MSC:

86A32 Geostatistics
62P12 Applications of statistics to environmental and related topics
62M07 Non-Markovian processes: hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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[1] Apostolides, A., Broadberry, S., Campbell, B., Overton, M. and van Leeuwen, B. (2008). English gross domestic product, 1300-1700: Some preliminary estimates. Working paper, Univ. Warwick.
[2] Appleby, A. B. (1981). Epidemics and famine in the Little Ice Age. In Climate and History (R. I. Rotberg and T. K. Rabb, eds.). Princeton Univ. Press, Princeton.
[3] Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica 66 47-78. · Zbl 1056.62523 · doi:10.2307/2998540
[4] Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. J. Appl. Econometrics 18 1-22.
[5] Barry, D. and Hartigan, J. A. (1993). A Bayesian analysis for change point problems. J. Amer. Statist. Assoc. 88 309-319. · Zbl 0775.62065 · doi:10.2307/2290726
[6] Brázdil, R., Pfister, C. and Luterbacher, J. (2005). Historical climatology in Europe-The state of the art. Clim. Change 70 363-430.
[7] Brown, D. M. (2000). The fate of Greenland’s Vikings. Archaeology . Available at .
[8] Burroughs, W. J. (2003). Weather Cycles : Real or Imaginary? , 2nd ed. Cambridge Univ. Press, Cambridge.
[9] Campbell, B. M. S. (2007). Three centuries of English crops yields, 1211-1491. Available at .
[10] Charles, A., Darné, O. and Kim, J. H. (2011). Small sample properties of alternative tests for martingale difference hypothesis. Econom. Lett. 110 151-154. · Zbl 1209.62199 · doi:10.1016/j.econlet.2010.11.018
[11] Clark, G. (2004). The price history of English agriculture, 1209-1914. Res. Econ. Hist. 22 41-123.
[12] de Vries, J. (1981). Measuring the impact of climate on history: The search for appropriate methodologies. In Climate and History (R. I. Rotberg and T. K. Rabb, eds.). Princeton Univ. Press, Princeton.
[13] Dierckx, G. and Teugels, J. L. (2010). Change point analysis of extreme values. Environmetrics 21 661-686. · doi:10.1002/env.1041
[14] Dobrovolný, P., Moberg, A., Brázdil, R., Pfister, C., Glaser, R., Wilson, R., Engelen, A., Limanówka, D., Kiss, A., Halíčková, M., Macková, J., Riemann, D., Luterbacher, J. and Böhm, R. (2010). Monthly, seasonal and annual temperature reconstructions for Central Europe derived from documentary evidence and instrumental records since AD 1500. Clim. Change 101 69-107.
[15] Durlauf, S. N. (1991). Spectral based testing of the martingale hypothesis. J. Econometrics 50 355-376. · Zbl 0757.62047 · doi:10.1016/0304-4076(91)90025-9
[16] Erdman, C. and Emerson, J. W. (2007). bcp: An R package for performing a Bayesian analysis of change point problems. J. Stat. Softw. 23 1-13.
[17] Escanciano, J. C. and Lobato, I. N. (2009a). Testing the martingale hypothesis. In Palgrave Handbook of Econometrics (T. C. Mills and K. Patterson, eds.). Applied Econometrics 2 . Palgrave Macmillan, London.
[18] Escanciano, J. C. and Lobato, I. N. (2009b). An automatic Portmanteau test for serial correlation. J. Econometrics 151 140-149. · Zbl 1431.62365 · doi:10.1016/j.jeconom.2009.03.001
[19] Escanciano, J. C. and Velasco, C. (2006). Generalized spectral tests for the martingale difference hypothesis. J. Econometrics 134 151-185. · Zbl 1157.62488 · doi:10.1016/j.jeconom.2005.06.019
[20] Glaser, R. and Riemann, D. (2009). A thousand year record of climate variation for Central Europe at a monthly resolution. Journal of Quartenary Science 24 437-449.
[21] Jones, P. D., Lister, D. H., Osborn, T. J., Harpham, C., Salmon, M. and Morice, C. P. (2012). Hemispheric and large-scale land-surface air temperature variations: An extensive revision and an update to 2010. J. Geophys. Res. 117 D05127.
[22] Kelly, M. and Ó Gráda, C. (2014). Supplement to “Change points and temporal dependence in reconstructions of annual temperature: Did Europe experience a Little Ice Age?” , DOI:10.1214/14-AOAS753SUPPB . · Zbl 1303.86005
[23] Kelly, M. and Ó Gráda, C. (2014c). Living standards and mortality since the Middle Ages. Econ. Hist. Rev. 67 358-381.
[24] Kim, J. H. (2009). Automatic variance ratio test under conditional heteroskedasticity. Finance Res. Lett. 6 179-185.
[25] Kim, J. H. (2010). vrtest: Variance ratio tests and other tests for martigale difference hypothesis. R package, available at .
[26] Lamb, H. H. (1995). Climate , History and the Modern World , 2nd ed. Routledge, London.
[27] Lo, A. W. and MacKinlay, A. C. (1989). The size and power of the variance ratio test in finite samples: A Monte Carlo investigation. J. Econometrics 40 203-238. · doi:10.1016/0304-4076(89)90083-3
[28] Luterbacher, J., Dietrich, D., Xoplaki, E., Grosjean, M. and Wanner, H. (2004). European seasonal and annual temperature variability, trends, and extremes since 1500. Science 303 1499-1503.
[29] Maddison, A. (2009). Statistics on World Population, GDP and Per Capita GDP, 1-2006 AD. Available at .
[30] Manley, G. (1974). Central England temperatures: Monthly means 1659 to 1973. Q. J. R. Meteorol. Soc. 100 389-405.
[31] Mann, M. E. (2002). Little Ice Age. In Encyclopedia of Global Environmental Change (M. C. McCracken and J. S. Perry, eds.). Wiley, New York.
[32] Mann, M. E., Zhang, Z., Rutherford, S., Bradley, R. S., Hughes, M. K., Shindell, D., Ammann, C., Faluvegi, G. and Ni, F. (2009). Global signatures and dynamical origins of the Little Ice Age and Medieval Climate Anomaly. Science 326 1256-1260.
[33] Matthes, F. E. (1939). Report of committee on glaciers, April 1939. Trans. Am. Geophys. Union 20 518-523.
[34] Matthews, J. A. and Briffa, K. R. (2005). The “Little Ice Age:” Re-evaluation of an evolving concept. Geografiska Annaler 87 A 17-36.
[35] McGovern, T. H. (1981). The economics of extinction in Norse Greenland. In Climate and History (T. M. L. Wrigley, M. J. Ingram and G. Farmer, eds.) 404-433. Cambridge Univ. Press, Cambridge.
[36] McShane, B. B. and Wyner, A. J. (2011). A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? Ann. Appl. Stat. 5 5-44. · Zbl 1220.62150 · doi:10.1214/10-AOAS398
[37] Miskimin, H. A. (1975). The Economy of Early Renaissance Europe , 1300 - 1460. Cambridge Univ. Press, Cambridge.
[38] PAGES 2k Consortium (2013). Continental-scale temperature variability during the past two millennia. Nat. Geosci. 6 339-346.
[39] Parker, G. (2008). Crisis and catastrophe: The global crisis of the seventeenth century reconsidered. Am. Hist. Rev. 113 1053-1079.
[40] Pfister, C. (1992). Monthly temperature and precipitation in Central Europe 1525-1979. In Climate Since A.D. 1500 (R. S. Bradley and P. D. Jones, eds.). Routledge, London.
[41] Schneer, J. (2005). The Thames . Yale Univ. Press, New Haven, CT.
[42] Sen, A. and Srivastava, M. S. (1975). On tests for detecting change in mean. Ann. Statist. 3 98-108. · Zbl 0305.62014 · doi:10.1214/aos/1176343001
[43] Slutsky, E. E. (1937). The summation of random causes as the source of cyclic processes. Econometrica 5 105-146.
[44] Teraesvirta, T., Lin, C. F. and Granger, C. W. J. (1993). Power of the neural network linearity test. J. Time Series Anal. 14 209-220.
[45] Trapletti, A. and Hornik, K. (2010). tseries: Time series analysis and computational finance. R package.
[46] van Engelen, A. F. V., Buisman, J. and IJnsen, F. (2001). A millennium of weather, winds and water in the low countries. In History and Climate : Memories of the Future? (P. D. Jones, A. E. J. Ogilvie, T. D. Davies and K. R. Briffa, eds.). Kluwer Academic, Boston, MA.
[47] Venkatraman, E. S. and Olshen, A. B. (2007). A faster circular binary segmentation algorithm for the analysis of array CGH data. Bioinformatics 23 657-663.
[48] Wanner, H., Beer, J., Bütikofer, J., Crowley, T. J., Cubasch, U., Flückiger, J., Goosse, H., Grosjean, M., Joos, F., Kaplan, J. O., Küttel, M., Müller, S. A., Prentice, C. I., Solomina, O., Stocker, T. F., Tarasov, P., Wagner, M. and Widmann, M. (2008). Mid- to late-holocene climate change-An overview. Quat. Sci. Rev. 27 1791-1828.
[49] Zeileis, A., Leisch, F., Hornik, K. and Kleiber, C. (2002). Strucchange: An R package for testing for structural change in linear regression models. J. Stat. Softw. 7 1-38.
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