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An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models

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Abstract

The annual temperatures recorded for the last two centuries in fifteen european stations around the Alps are analyzed. They show a global warming whose growth rate is not however constant in time. An analysis based on linear Arima models does not provide accurate results. Thus, we propose threshold nonlinear nonstationary models based on several regimes both in time and in levels. Such models fit all series satisfactorily, allow a closer description of the temperature changes evolution, and help to discover the essential differences in the behavior of the different stations.

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References

  • Auer I, Böhm R, Jurkovic A, Lipa W, Orlik A, Potzmann R, Schöner W, Ungersböck M, Matulla C, Briffa K, Jones PD, Efthymiadis D, Brunetti M, Nanni T, Maugeri M, Mercalli L, Mestre O, Moisselin J-M, Begert M, Müller-Westermeier G, Kveton V, Bochnicek O, Stastny P, Lapin M, Szalai S, Szentimrey T, Cegnar T, Dolinar M, Gajic-Capka M, Zaninovic K, Majstorovic Z, Nieplova E (2007) HISTALP— historical instrumental climatological surface time series of the Greater Alpine Region. Int J Climatol 27: 17–46

    Article  Google Scholar 

  • Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66: 47–78

    Article  MathSciNet  MATH  Google Scholar 

  • Baragona R, Battaglia F, Cucina D (2004) Fitting piecewise linear threshold autoregressive models by means of genetic algorithms. Comput Stat Data Anal 47: 277–295

    Article  MathSciNet  MATH  Google Scholar 

  • Baragona R, Battaglia F, Poli I (2011) Evolutionary statistical procedures. Springer, Berlin

    Book  MATH  Google Scholar 

  • Battaglia F, Protopapas MK (2011) Time-varying multi-regime models fitting by genetic algorithms. J Time Ser Anal 32: 237–252

    Article  MathSciNet  Google Scholar 

  • Battaglia F, Protopapas MK (2012) Multi-regime models for nonlinear nonstationary time series. Comput Stat 27: 319–341

    Article  MathSciNet  Google Scholar 

  • Bhansali RJ, Downham DY (1977) Some properties of the order of an autoregressive model selected by a generalization of Akaike’s EPF criterion. Biometrika 64: 547–551

    MathSciNet  MATH  Google Scholar 

  • Böhm R, Auer I, Brunetti M, Maugeri M, Nanni T, Schöner W (2001) Regional temperature variability in the European Alps: 1760–1998 from homogenized instrumental time series. Int J Climatol 21: 1779–1801

    Article  MATH  Google Scholar 

  • Böhm R, Jones PD, Hiebl J, Frank D, Brunetti M, Maugeri M (2010) The early instrumental warm-bias: a solution for long central European temperature series 1760–2007. Clim Change 101: 41–67

    Article  Google Scholar 

  • Cai Z, Fan J, Yao Q (2000) Functional coefficient regression models for nonlinear time series. J Am Stat Assoc 95: 941–955

    Article  MathSciNet  MATH  Google Scholar 

  • Chan KS, Tong H (1986) On estimating thresholds in autoregressive models. J Time Ser Anal 7: 179–190

    Article  MathSciNet  MATH  Google Scholar 

  • Chan KS, Tong H (1990) On the likelihood ratio tests for threshold autoregression. J R Stat Soc B 52: 469–476

    MathSciNet  MATH  Google Scholar 

  • Chatterjee S, Laudato M, Lynch LA (1996) Genetic algorithms and their statistical applications an introduction. Comput Stat Data Anal 22: 633–651

    Article  MATH  Google Scholar 

  • Chen C, Liu LM (1993) Joint estimation of model parameters and outlier effects in time series. J Am Stat Assoc 88: 284–297

    Article  MATH  Google Scholar 

  • Chen R, Tsay R (1993) Functional coefficient autoregressive models. J Am Stat Assoc 88: 298–308

    Article  MathSciNet  MATH  Google Scholar 

  • Crawford KD, Wainwright RL (1995) Applying genetic algorithms to outlier detection. In: Eshelman LJ (ed) Proceedings of the sixth international conference on genetic algorithms. Morgan Kaufmann, San Mateo, CA, pp 546-550

  • Davis R, Lee T, Rodriguez-Yam G (2006) Structural break estimation for nonstationary time series models. J Am Stat Assoc 101: 223–239

    Article  MathSciNet  MATH  Google Scholar 

  • Dueker MJ, Sola M, Spagnolo F (2007) Contemporaneous threshold autoregressive models: estimation, testing and forecasting. J Econom 141: 517–547

    Article  MathSciNet  Google Scholar 

  • European Environment Agency (2008) Impacts of Europe’s changing climate—2008 indicator-based assessment. EEA report no. 4/2008. http://www.eea.europa.eu. ISBN 978-92-9167-372-8

  • Gaetan C (2000) Subset ARMA model identification using genetic algorithms. J Time Ser Anal 21: 559–570

    Article  MathSciNet  MATH  Google Scholar 

  • Hamilton J (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57: 357–384

    Article  MathSciNet  MATH  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • IPCC Core Writing Team, Pachauri RK, Reisinger A (eds) (2007) Climate change 2007: synthesis report. Contribution of working groups I, II and III to the fourth assessment report of the intergovernmental panel on climate change. IPCC, Geneva. ISBN 92-9169-122-4

  • Kamgaing JT, Ombao H, Davis RA (2009) Autoregressive processes with data-driven regime switching. J Time Ser Anal 30: 505–533

    Article  MATH  Google Scholar 

  • Kennedy J, Eberhart R (2001) Swarm intelligence. Morgan Kaufman, San Mateo

    Google Scholar 

  • Lin C, Teräsvirta T (1994) Testing the constancy of regression parameters against continuous structural change. J Econom 62: 211–228

    Article  MATH  Google Scholar 

  • Lundbergh S, Teräsvirta T, van Dijk D (2003) Time-varying smooth transition autoregressive models. J Bus Econ Stat 21:104–121

    Article  Google Scholar 

  • Marcellino M, Rossi B (2008) Model selection for nested and overlapping nonlinear, dynamic and possibly mis-specified models. Oxford Bull Econ Stat 70(Suppl): 867–893

    Article  Google Scholar 

  • Price KV, Storn R, Lampinen J (2005) Differential evolution, a practical approach to global optimization. Springer, Berlin

    MATH  Google Scholar 

  • Priestley MB (1988) Non-linear and non-stationary time series analysis. Academic Press, London

    Google Scholar 

  • Reeves CR, Rowe JE (2003) Genetic algorithms—principles and perspective a guide to GA theory. Kluwer, London

    Google Scholar 

  • Rissanen J (2007) Information and complexity in statistical models. Springer, Berlin

    Google Scholar 

  • Rivers D, Vuong Q (2002) Model selection tests for nonlinear dynamic models. Econom J 5: 1–39

    Article  MathSciNet  MATH  Google Scholar 

  • Sin C-Y, White H (1996) Information criteria for selecting possibly misspecified parametric models. J Econom 71: 207–225

    Article  MathSciNet  MATH  Google Scholar 

  • Teräsvirta T (1994) Specification estimation and evaluation of smooth transition autoregressive models. J Am Stat Assoc 89: 208–218

    Google Scholar 

  • Teräsvirta T (1998) Modeling economic relationships with smooth transition regression. In: Ullah A, Giles DEA (eds) Handbook of applied economic statistics. Marcel Dekker, New York, pp 507–552

    Google Scholar 

  • Tong H (1990) Non linear time series: a dynamical system approach. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Tong H, Lim K (1980) Threshold autoregression, limit cycles and ciclical data. J R Stat Soc Ser B 42: 245–292

    MATH  Google Scholar 

  • Tsay RS (1988) Outliers, level shifts and variance changes. J Forecast 7: 1–20

    Article  Google Scholar 

  • Wu B, Chang CL (2002) Using genetic algorithms to parameters (d,r) estimation for threshold autoregressive models. Comput Stat Data Anal 38: 315–330

    Article  MathSciNet  MATH  Google Scholar 

  • Wu S, Chen R (2007) Threshold variable determination and threshold variable driven switching autoregressive models. Stat Sin 17: 241–264

    MATH  Google Scholar 

  • Zebisch M, Zimmermann P, Böhm R, Schöner W (2009) Climate change in the Alps. In: Regional climate change and adaptation—the Alps facing the challenge of changing water resources. European Environment Agency report no. 8/2009. http://www.eea.europa.eu. ISBN 978-92-9213-006-0

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche, University La Sapienza, Rome, Italy

    Francesco Battaglia & Mattheos K. Protopapas

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  1. Francesco Battaglia
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  2. Mattheos K. Protopapas
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Correspondence to Francesco Battaglia.

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Battaglia, F., Protopapas, M.K. An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models. Stat Methods Appl 21, 315–334 (2012). https://doi.org/10.1007/s10260-012-0200-9

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