This paper deals with the analysis of the temperatures in a group of 29 stations located in twelve European countries by looking at the coefficients in a linear time trend regression model and allowing for long memory patterns in the error term. The results indicate that long memory is present in practically all cases, and the time trend coefficients are statistically significant in the majority of the cases implying evidence of increasing warming trends. This pattern is particularly noticeable in the case of several stations located across Italy and France, which might be related with micro climates affecting these regions.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
I(1) denotes integration of order 1, which means that the series needs to be first differenced to render it stationary I(0). This latter concept (I(0)) is considered as a minimal requirement in time series to make statistical inference. Fractional integration or I(d) takes place when the number of differences required in the series is d and d is a fractional value.
Long memory is a feature of the I(d, d > 0) models that is characterized by the large degree of association between observations which are far distant in time. Mean reversion means that shocks will be transitory disappearing in the long run and takes place when d < 1.
A description of the functional form of this method can be found in Gil-Alana and Robinson (1997).
The length of the series varies from 67 to 359 observations. Nevertheless, the method employed in the paper, in spite of its asymptotic nature, it performs well even in small samples as it was shown in Gil-Alana and Robinson (1997) and other papers.
In other words, if you do a 30 hypothesis tests at P[Type-1 error] = 10%, you will end up rejecting about 3 of the hypothesis where the null is actually true, simply because the test is set up that way. The same situation holds for confidence intervals: the 95% confidence intervals will fail to contain the true value in 5 of every 100 cases just because such intervals are designed for a single case, not multiple times usage. Thus, the 95% intervals reported across Tables 1 and 2 contain a non-ignorable number of false positives.
The spectral density function is basically the frequency domain representation of the autocovariances based on Fourier transforms.
Once more note that the results for Navacerrada (NAVA), Salamanca (SALA) and Cadiz (CADI) should be taken with caution.
Baillie RT, Chung SK (2002) Modelling and forecasting from trend-stationary long memory models with applications to climatology. Int J Forecast 18(2):215–226
Bloomfield P (1973) An exponential model in the spectrum of a scalar time series. Biometrika 60(2):217–226
Brunet M, Jones PD, Sigró J, Saladié O, Aguilar E, Moberg A, Della-Marta PM, Lister D, Walther A, López D (2007) Temporal and spatial temperature variability and change over Spain during 1850–2005. J Geophys Res-Atmos 112(D12):1–28. https://doi.org/10.1029/2006JD008249
Bunde A, Havlin S, Koscielny-Bunde E, Schellnhuber HJ (2001) Long term persistence in the atmosphere: global laws and tests of climate models. Phys A: Stat Mech Applic 302(1-4):255–267
Bunde A, Eichner JF, Kantelhardt JW, Havlin S (2005) Long term memory: a natural mechanism for the clustering of extreme events and anomalous residual times in climate records. Phys Rev Lett 94(4):048701
Caballero R, Jewson S, Brix A (2002) Long memory in surface air temperature: Detection, modelling and application to weather derivative valuation. Clim Res 21(2):127–140
Caloiero T, Coscarelli R, Ferrari E, Sirangelo B (2017) Trend analysis of monthly mean values and extreme indices of daily temperature in a region of southern Italy. Int J Climatol 37(S1):284–297. https://doi.org/10.1002/joc.5003
Dahlhaus R (1989) Efficient parameter estimation for self-similar processes. Ann Stat 17(4):1749–1766
Delvaux C, Ingels R, Vrábeĺ V, Journée M, Bertrand C (2018) Quality control and homogenization of the Belgian historical temperature data. Int J Climatol. https://doi.org/10.1002/joc.5792
Franzke C (2010) Long range dependence and climate noise characteristics of Antarctic temperature data. J Clim 23(22):6074–6081
Franzke C (2012) Nonlinear trends, long-range dependence, and climate noise properties of surface temperature. J Clim 25(12):4172–4183
Gibelin A-L, Dubuisson B, Corre L, Deaux N, Jourdain S, Laval L, Piquemal J-M, Mestre O, Dennetière D, Desmidt S, Tamburini A (2014) Evolution de la température en France depuis les années 1950: Constitution d’un nouveau jeu de séries homogénéisées de référence. La Météorologie 87:45–53. https://doi.org/10.4267/2042/54336
Gil-Alana LA (2003) An application of fractional integration to a long temperature time series. Int J Climatol 23(14):1699–1710
Gil-Alana LA (2004) The use of the Bloomfield model as an approximation to ARMA processes in the context of fractional integration. Math Comput Model 39(4-5):429.436
Gil-Alana LA (2005) Statistical model for the temperatures in the Northern hemisphere using fractional integration techniques. J Clim 18(24):5537–5369
Gil-Alana LA (2008) Time trend estimation with breaks in temperature time series. Clim Chang 89(3-4):325–337
Gil-Alana LA (2010) Climate change in the Iberian Peninsula. Evidence based on fractional integration techniques. Seguridad y Medio Ambiente 117(1):50–62
Gil-Alana LA (2018) Maximum and minimum temperatures in the United States: time trends and persistence. Atmos Sci Lett 19(4):e810, 1−3. https://doi.org/10.1002/asl.810
Gil-Alana LA, Robinson PM (1997) Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. J Econ 80:241–268
IPCC (2014) Climate Change 2014: synthesis report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. IPCC, Geneva, Switzerland, 151 pp
Klingbjer P, Moberg A (2003) A composite monthly temperature record from Tornedalen in northern Sweden, 1802−2002. Int J Climatol 23(12):1465–1494. https://doi.org/10.1002/joc.946
Mariani, L., and Zavatti, F. (2017), A dataset of the European average temperature anomalies for the period 1655-2016, Climatemonitor.
Matiu M, Ankerst DP, Menzel A (2016) Asymmetric trends in seasonal temperature variability in instrumental records from ten stations in Switzerland, Germany and the UK from 1864 to 2012. Int J Climatol 36(1):13–27. https://doi.org/10.1002/joc.4326
Nemec J, Gruber C, Chimani B, Auer I (2013) Trends in extreme temperature indices in Austria based on a new homogenised dataset. Int J Climatol 33(6):1538–1550. https://doi.org/10.1002/joc.3532
Rea W, Reale M, Brown J (2011) Long memory in temperature reconstructions. Climate Change 107(3-4):247–265
Ribes A, Corre L, Gibelin A-L, Dubuisson B (2016) Issues in estimating observed change at the local scale – a case study: the recent warming over France. Int J Climatol 36(11):3794–3806. https://doi.org/10.1002/joc.4593
Robinson PM (1994) Efficient Tests of Nonstationary Hypotheses. J Am Stat Assoc 89(428):1420–1437
Scorzini AR, Di Bacco M, Leopardi M (2018) Recent trends in daily temperature extremes over the central Adriatic region of Italy in a Mediterranean climatic context. Int J Climatol 38(S1):e741–e757. https://doi.org/10.1002/joc.5403
Shen Z, Shi J, Lei Y (2017) Comparison of the long range climate memory in outgoing lognwage radiation over the Tibetan plateau and the Indian monsoon region. Adv Meteorol 7637351:1–7
Whittle P (1951) Hypothesis testing in time series analysis. Uppsala, Almqvist & Wiksells Boktrycheri AB
Yuan N, Fu Z, Liu S (2013) Long-term memory in climate variability: a new look based on fractional integral techniques. J Geophys Res-Atmos 118(23):12962–12969
Yuan N, Ding M, Huang Y (2015) On the long term climate memory in the surface air temperature records over Antarctica: a non-negligible factor for trend evaluation. J Clim 28(15):5922–5934
Comments from the Editor and three anonymous reviewers are gratefully acknowledged.
Prof. Luis A. Gil-Alana gratefully acknowledges financial support from the Ministerio de Economía y Competitividad (ECO2017-85503-R).
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Gil-Alana, L.A., Sauci, L. Temperatures across Europe: evidence of time trends. Climatic Change 157, 355–364 (2019). https://doi.org/10.1007/s10584-019-02568-6
- European temperatures
- Long memory
- Time trends