IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v183y2020i3p883-908.html
   My bibliography  Save this article

How does temperature vary over time?: evidence on the stationary and fractal nature of temperature fluctuations

Author

Listed:
  • John K. Dagsvik
  • Mariachiara Fortuna
  • Sigmund Hov Moen

Abstract

The paper analyses temperature data from 96 selected weather stations world wide, and from reconstructed northern hemisphere temperature data over the last two millennia. Using a non‐parametric test, we find that the stationarity hypothesis is not rejected by the data. Subsequently, we investigate further properties of the data by means of a statistical model known as the fractional Gaussian noise (FGN) model. Under stationarity FGN follows from the fact that the observed data are obtained as temporal aggregates of data generated at a finer (basic) timescale where temporal aggregation is taken over a ‘large’ number of basic units. The FGN process exhibits long‐range dependence. Several tests show that both the reconstructed and most of the observed data are consistent with the FGN model.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:183:y:2020:i:3:p:883-908
    DOI: 10.1111/rssa.12557
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssa.12557
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssa.12557?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Rea, William & Oxley, Les & Reale, Marco & Brown, Jennifer, 2013. "Not all estimators are born equal: The empirical properties of some estimators of long memory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 29-42.
    2. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 382-416, April.
    3. Magne Aldrin & Marit Holden & Peter Guttorp & Ragnhild Bieltvedt Skeie & Gunnar Myhre & Terje Koren Berntsen, 2012. "Bayesian estimation of climate sensitivity based on a simple climate model fitted to observations of hemispheric temperatures and global ocean heat content," Environmetrics, John Wiley & Sons, Ltd., vol. 23(3), pages 253-271, May.
    4. Anders Moberg & Dmitry M. Sonechkin & Karin Holmgren & Nina M. Datsenko & Wibjörn Karlén & Stein-Erik Lauritzen, 2006. "Correction: Corrigendum: Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data," Nature, Nature, vol. 439(7079), pages 1014-1014, February.
    5. James E. H. Davidson & David B. Stephenson & Alemtsehai A. Turasie, 2016. "Time series modeling of paleoclimate data," Environmetrics, John Wiley & Sons, Ltd., vol. 27(1), pages 55-65, February.
    6. 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.
    7. 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.
    8. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    2. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    3. Federico Maddanu, 2023. "Forecasting highly persistent time series with bounded spectrum processes," Statistical Papers, Springer, vol. 64(1), pages 285-319, February.
    4. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Laura Mayoral, 2007. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 124-148, March.
    2. J. Eduardo Vera-Valdés, 2021. "Temperature Anomalies, Long Memory, and Aggregation," Econometrics, MDPI, vol. 9(1), pages 1-22, March.
    3. 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).
    4. S. D. Grose & D. S. Poskitt, 2006. "The Finite-Sample Properties of Autoregressive Approximations of Fractionally-Integrated and Non-Invertible Processes," Monash Econometrics and Business Statistics Working Papers 15/06, Monash University, Department of Econometrics and Business Statistics.
    5. William Rea & Marco Reale & Jennifer Brown, 2011. "Long memory in temperature reconstructions," Climatic Change, Springer, vol. 107(3), pages 247-265, August.
    6. Richard T. Baillie & George Kapetanios & Fotis Papailias, 2017. "Inference for impulse response coefficients from multivariate fractionally integrated processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 60-84, March.
    7. 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.
    8. Beran, Jan & Feng, Yuanhua, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Papers 99/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    9. repec:wyi:journl:002087 is not listed on IDEAS
    10. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2022. "Globalization, long memory, and real interest rate convergence: a historical perspective," Empirical Economics, Springer, vol. 63(5), pages 2331-2355, November.
    11. Luis A. Gil-Alana & Laura Sauci, 2019. "Temperatures across Europe: evidence of time trends," Climatic Change, Springer, vol. 157(3), pages 355-364, December.
    12. Baillie, Richard T. & Kapetanios, George & Papailias, Fotis, 2014. "Bandwidth selection by cross-validation for forecasting long memory financial time series," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 129-143.
    13. Rea, William & Reale, Marco & Brown, Jennifer & Oxley, Les, 2011. "Long memory or shifting means in geophysical time series?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1441-1453.
    14. Claudio, Morana & Giacomo, Sbrana, 2017. "Some Financial Implications of Global Warming: An Empirical Assessment," Working Papers 377, University of Milano-Bicocca, Department of Economics, revised 25 Dec 2017.
    15. Claudio, Morana & Giacomo, Sbrana, 2017. "Temperature anomalies, radiative forcing and ENSO," Working Papers 361, University of Milano-Bicocca, Department of Economics, revised 10 Feb 2017.
    16. 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.
    17. Giraitis, Liudas & Phillips, Peter C.B., 2012. "Mean and autocovariance function estimation near the boundary of stationarity," Journal of Econometrics, Elsevier, vol. 169(2), pages 166-178.
    18. Bai, Shuyang & Taqqu, Murad S., 2019. "Sensitivity of the Hermite rank," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 822-840.
    19. Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.
    20. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona School of Economics.
    21. Terence C. Mills, 2012. "Semi-parametric modelling of temperature records," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 361-383, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssa:v:183:y:2020:i:3:p:883-908. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.