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Long memory, seasonality and time trends in the average monthly temperatures in Alaska

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Abstract

This paper deals with the analysis of monthly temperatures in 19 meteorological stations in Alaska during the last 50 years. For this purpose, we employ a procedure that permits us to examine in a single framework several features observed in climatological time series such as time trends, long-range persistence and seasonality. The results indicate that the highest degrees of persistence are observed in stations located in the southern regions and seasonality appears as a major issue in all cases. Removing the seasonal structure and focussing on the anomalies with respect to the monthly means, the time trend coefficients appear significantly positive in the majority of the cases, implying that temperatures have increased during the last 50 years.

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Notes

  1. First-order stations are defined as those operated by certified observers and most often operated by the National Weather Service.

  2. Though not displayed, the I(d) model also admits an infinite MA representation.

  3. Note that we use subscripts in d and ρ (d s and ρ s ) when referring to the parameters in the seasonal processes.

  4. Additionally, both models ((M1) and (M2)) can be expressed as infinite AR processes, implying that the present value can be expressed as a function of all its past observations.

  5. Longer time periods are available at this website. However, we have only considered those data that do not contain missing values.

  6. Note that though Robinson (1994) is a testing procedure, we may also use it as an estimation method by choosing the value of d (or d s ) that produces the lowest statistic in absolute value for a range of d–(d s ) values. Moreover, the estimation of the time trend coefficients is based on standard OLS/GLS methods since under the null hypothesis the model is supposed to be I(0) and thus well behaved. (See Robinson 1994). On the other hand, the series are long enough to justify the use of I(d) techniques.

  7. That means that for these four series we cannot reject a deterministic trend model with seasonal AR(1) disturbances. However, for the remaining series, this model is decisively rejected in favour of a long memory specification.

  8. That is, the increase in the temperatures ranges between 2.058°F (1.140°C) and 4.230°F (2.346°C) over the last 50 years.

  9. Anti-persistence means that the series reverses itself more often than a random series would.

  10. Note that (1 − L s)ds can be decomposed into (1 − L)ds and S(L)ds, where \( S(L) = \left( {1 + L + {L^2} + \ldots {L^{{s - 1}}}} \right) \) contains the seasonal frequencies.

  11. Note that this way of removing the seasonality imposes that this is of a deterministic nature as opposed to the cases presented above where the seasonal structure was supposed to be stochastic.

  12. This is consistent with the empirical results obtained in many other papers.

References

  • Bloomfield P (1992) Trends in global temperatures. Clim Chang 21:1–16

    Article  Google Scholar 

  • Bloomfield P, Nychka D (1992) Climate spectra and detecting climate change. Clim Chang 21:275–287

    Article  Google Scholar 

  • Chapman W, Walsh J (1993) Recent variation in sea ice and air temperature at high latitudes. BAMS 94:33–48

    Article  Google Scholar 

  • Diebold FX, Inoue A (2001) Long memory and regime switching. J Econ 105:131–159

    Google Scholar 

  • Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 13:253–263

    Article  Google Scholar 

  • Fischer C, Gil-Alana LA (2009) International travelling and trade: further evidence for the case of Spanish wine based on fractional VAR specifications. Applied Economics 42:2417–2434

    Google Scholar 

  • Fomby T, Vogelsang T (2002) The application of size robust trend statistics to global warming temperature series. J Clim 15:117–123

    Article  Google Scholar 

  • Ghil M, Vautard R (1991) Interdecadal oscillations and the warming trend in global temperature time series. Nature 350:324–327

    Article  Google Scholar 

  • Gil-Alana LA (2002) Seasonal long memory in the aggregate output. Econ Lett 74:333–337

    Article  Google Scholar 

  • Gil-Alana LA (2003) An application of fractional integration to a long temperature time series. Int J Climatol 23:1699–1710

    Article  Google Scholar 

  • Gil-Alana LA (2004) The use of the Bloomfield (1973) model as an approximation to ARMA processes in the context of fractional integration. Math Comput Model 29(4/5):429–436

    Article  Google Scholar 

  • Gil-Alana LA (2005) Statistical model of the temperatures in the northern hemisphere using fractional integration techniques. J Clim 18:5357–5369

    Article  Google Scholar 

  • Gil-Alana LA, Robinson PM (1997) Testing unit roots and other nonstationary hypotheses in macroeconomic time series. J Econ 80:241–268

    Google Scholar 

  • Gil-Alana LA, Robinson PM (2001) Testing of seasonal fractional integration in the UK and Japanese consumption and income. J Appl Econ 16:95–114

    Article  Google Scholar 

  • Granger CWJ (1980) Long memory relationships and the aggregation of dynamic models. J Econ 14:227–238

    Google Scholar 

  • Gray HL, Yhang N, Woodward WA (1989) On generalized fractional processes. J Time Anal 10:233–257

    Article  Google Scholar 

  • Gray HL, Yhang N, Woodward WA (1994) A correction: on generalized fractional processes. J Time Anal 15:561–562

    Article  Google Scholar 

  • Grenander U, Rosenblatt M (1957) Statistical analysis of stationary time series. Chelsea Publishing Company, New York

    Google Scholar 

  • Hamilton JD (1994) Time series analysis. Princeton University Press, Princeton, p 820

    Google Scholar 

  • Hansen J, Lebedeff S (1987) Global trends of measured surface air temperature. J Geophys Res 92:345–372

    Article  Google Scholar 

  • Hansen J, Lebedeff S (1988) Global surface air temperatures. Update through 1987. Geophys Lett 15:323–326

    Article  Google Scholar 

  • Hartmann B, Wendler G (2005) The significance of the 1976 Pacific climate shift in the climatology of Alaska. J Clim 18(4824):4839

    Google Scholar 

  • Harvey DI, Mills TC (2001) Modelling global temperature trends using cointegration and smooth transition. Stat Model 1:143–159

    Article  Google Scholar 

  • Harvey DI, Leybourne SJ, Newbold P (1997) Testing the equality of prediction mean squared errors. Int J Forecast 13:281–291

    Article  Google Scholar 

  • Hasselmann K (1993) Optimal fingerprints for the detection of time dependent climate change. J Clim 6:1957–1971

    Article  Google Scholar 

  • Jones PD, Raper SCB, Wigley TML (1986) Southern hemisphere surface air temperature variations: 1851–1984. J Clim Appl Meteorol 25(9):1213–1230

    Article  Google Scholar 

  • Jones PD, Osborn TJ, Briffa KR (1997) Estimating sampling errors in large scale temperature averages. J Clim 10:2548–2568

    Article  Google Scholar 

  • Jones PD, Parker DE, Osborn TJ, Briffa KR (2008) Global and hemispheric temperature anomalies–land and marine instrumental records. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, TN, USA

  • Juday GP (1984) Temperature trends in the Alaska climate records. Problems, updates and prospects. In Mc Beath JH (ed) The potential effects of carbon dioxide-induced climatic changes in Alaska, University of Alaska Agricultural Experimental Station Miscellaneous Publication 83, 176–191

  • Karoly D, Wu Q (2005) Detection of regional surface temperature trends. J Clim 18:4337–4343

    Article  Google Scholar 

  • Kaufmann RK, Stern DI (2002) Cointegration analysis of hemispheric temperature relations. J Geophys Res 107:4012

    Article  Google Scholar 

  • Kaufmann RK, Kauppi H, Stock JH (2006) The relation between radiative forcing and temperature: what do statistical analyses of the observational record measure? Clim Chang 77:279–289

    Article  Google Scholar 

  • Keimig FT, Bradley RS (2002) Recent changes in wind chill temperatures at high latitudes in North America. Geophys Res Lett. doi:10.1029/2001GL013228, Vol. 29 (8)

  • Koscielny-Bunde E, Bunde A, Havlin S, Roman HE, Goldreich Y, Schellnhuber HJ (1998) Indication of a universal persistence law governing atmospheric variability. Phys Rev Lett 81:729–732

    Article  Google Scholar 

  • Lewis PAW, Ray BK (1997) Modelling long-range dependence, nonlinearity and periodic phenomena in sea surface temperatures using TSMARS. J Am Stat Assoc 92:881–893

    Google Scholar 

  • Liu B, Xu M, Henderson M (2004) Taking China's temperature: daily range, warming trends and regional variations. J Clim 17:4453–4462

    Article  Google Scholar 

  • Maraun D, Rust HW, Timmer H (2004) Tempting long-memory on the interpretation of DFA results. Nonlinear Process Geophys 11:495–503

    Article  Google Scholar 

  • Mills TC (2007) Time series modelling of two millennia of northern hemisphere temperatures. J Roy Stat Soc Series A 170:83–94

    Google Scholar 

  • Neerchal NK, Brunenmeister SL (1993) Estimation of trend. In Patil GP, Rao CR (eds) Chesapeake Bay Water Quality Data, Multivariate Environmental Statistics. 407–421

  • Nicholls N, Gruza GV, Jouzel J, Karl TR, Ogallo LA, Parker DE (1996) Observed climate variability and change. In: Houghton JT, Filho LGM, Callander BA, Harris N, Kattenberg A, Maskell K (eds) Climate change 1995: the science of climate change. Cambridge University Press, Cambridge, pp 133–192

    Google Scholar 

  • North GR, Kim K-Y (1995a) Detection of forced climate signals. Part II. Simulation results. J Clim 6:409–417

    Article  Google Scholar 

  • North GR, Kim K-Y (1995b) Regional simulations of greenhouse warming including natural variability. Bull Am Meteorol Soc 76:2171–2178

    Article  Google Scholar 

  • North GR, Kim K-Y, Shen SP, Hardin JW (1995) Detection of forced climate signals. Part I. Filter theory. J Clim 6:401–408

    Article  Google Scholar 

  • Park RE, Mitchell BM (1980) Estimating the autocorrelated error model with trended data. J Econ 13:185–201

    Google Scholar 

  • Pelletier J, Turcotte D (1999) Self-affine time series II. Applications and models. Adv Geophys 40:91–166

    Article  Google Scholar 

  • Percival DB, Overland JE, Mofjeld HO (2001) Interpretation of North Pacific variability as a short- and long-memory process. J Clim 14:4545–4559

    Article  Google Scholar 

  • Percival DB, Overland JE, Mofjeld HO (2004) Modelling North Pacific climate time series. In: Brillinger DR, Robinson EA, Schoenberg FP (eds) Time series analysis and applications to geophysical systems, vol 139. Springer, Heidelberg pp, pp 151–167

    Chapter  Google Scholar 

  • Pethkar JS, Selvam AM (1997) Nonlinear dynamics and chaos. Applications for prediction of weather and climate. Proc. TROPMET 97, Bangalare, India

  • Porter-Hudak S (1990) An application of the seasonal fractionally differenced model to the monetary aggregate. J Am Stat Assoc 85:338–344

    Google Scholar 

  • Prais SJ, Winsten CB (1954) Trend estimators and serial correlation, Cowles Commission Monograph, no. 23. Yale University Press, New Haven, CT

    Google Scholar 

  • Robeson SM (2008) Trends in time-varying perceptiles of daily minimum and maximum temperature over North America. Geophys Res Lett 31:4

    Google Scholar 

  • Robinson PM (1978) Statistical inference for a random coefficient autoregressive model. Scand J Stat 5:163–168

    Google Scholar 

  • Robinson PM (1994) Efficient tests of nonstationary hypotheses. J Am Stat Assoc 89:1420–1437

    Google Scholar 

  • Schlesinger ME, Ramankutty N (1994) Low-frequency oscillation in the global climate system of period 65–70 years. Nature 367:723–727

    Article  Google Scholar 

  • Serreze MC, Walsh JE, Chapin FSIII, Osterkamp T, Dyurgerov M, Romanovsky V, Oechel WC, Morison J, Zhang T, Barry RG (2000) Observational evidence of recent change in the northern high-latitude environment. Clim Chang 46:159–207

    Article  Google Scholar 

  • Smith RL (1993) Long-range dependence and global warming. Statistics for the Environment (ed. Barnett V, Turkman KF pub. J. Wiley), 141–161

  • Stafford J, Wendler G, Curtis J (2000) Temperature and precipitation of Alaska: 50 year. Trend analysis. Theor Appl Climatol 67:33–44

    Article  Google Scholar 

  • Stern ID, Kaufmann RK (2000) Is there a global warming signal in hemispheric temperature series? Clim Chang 47:411–438

    Article  Google Scholar 

  • Woodward WA, Gray HL (1993) Global warming and the problem of testing for trend in time series data. J Clim 6:953–962

    Article  Google Scholar 

  • Woodward WA, Gray HL (1995) Selecting a model for detecting the presence of a trend. J Clim 8:1929–1937

    Article  Google Scholar 

  • Zheng X, Basher RE, Thompson CS (1997) Trend detection in regional-mean temperature series. Maximum, minimum, mean, diurnal range and SST. J Clim 10:317–326

    Article  Google Scholar 

Download references

Acknowledgement

Comments from the editor and two anonymous referees are gratefully acknowledged. The author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2008-03035 ECON Y FINANZAS, Spain) and from a PIUNA Project from the University of Navarra.

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  1. Faculty of Economics, University of Navarra, Edificio Biblioteca, Entrada Este, 31080, Pamplona, Spain

    Luis A. Gil-Alana

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Gil-Alana, L.A. Long memory, seasonality and time trends in the average monthly temperatures in Alaska. Theor Appl Climatol 108, 385–396 (2012). https://doi.org/10.1007/s00704-011-0539-0

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