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Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?

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  • Terence C. Mills

Abstract

Summary. The time series properties of the temperature reconstruction of Moberg and co‐workers are analysed. It is found that the record appears to exhibit long memory characteristics that can be modelled by an autoregressive fractionally integrated moving average process that is both stationary and mean reverting, so that forecasts will eventually return to a constant underlying level. Recent research has suggested that long memory and shifts in level and trend may be confused with each other, and fitting models with slowly changing trends is found to remove the evidence of long memory. Discriminating between the two models is difficult, however, and the strikingly different forecasts that are implied by the two models point towards some intriguing research questions concerning the stochastic process driving this temperature reconstruction.

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  • Terence C. Mills, 2007. "Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 83-94, January.
    • Handle: RePEc:bla:jorssa:v:170:y:2007:i:1:p:83-94
    DOI: 10.1111/j.1467-985X.2006.00443.x
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    1. Mills, Terence C. & Crafts, N. F. R., 1996. "Trend Growth in British Industrial Output, 1700-1913: A Reappraisal," Explorations in Economic History, Elsevier, vol. 33(3), pages 277-295, July.
    2. Philip Hans Franses & Namwon Hyung, 2005. "Forecasting time series with long memory and level shifts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(1), pages 1-16.
    3. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    4. Smith, Aaron, 2005. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 321-335, July.
    5. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    6. David Harvey & Terence Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 675-683.
    7. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    8. Baillie, Richard T. & Chung, Sang-Kuck, 2002. "Modeling and forecasting from trend-stationary long memory models with applications to climatology," International Journal of Forecasting, Elsevier, vol. 18(2), pages 215-226.
    9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    10. Luis Gil-Alana, 2003. "Estimation of the degree of dependence in the temperatures in the northern hemisphere using semi-parametric techniques," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1021-1031.
    11. Anders Moberg & Dmitry M. Sonechkin & Karin Holmgren & Nina M. Datsenko & Wibjörn Karlén, 2005. "Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data," Nature, Nature, vol. 433(7026), pages 613-617, February.
    12. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
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    Cited by:

    1. J. Eduardo Vera-Valdés, 2021. "Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation," Econometrics, MDPI, vol. 9(4), pages 1-18, October.
    2. Gilles Dufrénot & William Ginn & Marc Pourroy, 2021. "The Effect of ENSO Shocks on Commodity Prices: A Multi-Time Scale Approach," Working Papers halshs-03225070, HAL.
    3. J. Eduardo Vera-Valdés, 2021. "Temperature Anomalies, Long Memory, and Aggregation," Econometrics, MDPI, vol. 9(1), pages 1-22, March.
    4. John K. Dagsvik & Mariachiara Fortuna & Sigmund Hov Moen, 2020. "How does temperature vary over time?: evidence on the stationary and fractal nature of temperature fluctuations," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 883-908, June.
    5. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Beenstock, Michael & Reingewertz, Yaniv & Paldor, Nathan, 2016. "Testing the historic tracking of climate models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1234-1246.
    7. William Rea & Marco Reale & Jennifer Brown, 2011. "Long memory in temperature reconstructions," Climatic Change, Springer, vol. 107(3), pages 247-265, August.
    8. Luis A. Gil-Alana, 2015. "Linear and segmented trends in sea surface temperature data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(7), pages 1531-1546, July.
    9. Terence C. Mills, 2012. "Semi-parametric modelling of temperature records," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 361-383, May.
    10. Michael Mann, 2011. "On long range dependence in global surface temperature series," Climatic Change, Springer, vol. 107(3), pages 267-276, August.

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