Theoretical and Applied Climatology

, Volume 108, Issue 3–4, pp 385–396 | Cite as

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

Original Paper


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.


  1. Bloomfield P (1992) Trends in global temperatures. Clim Chang 21:1–16CrossRefGoogle Scholar
  2. Bloomfield P, Nychka D (1992) Climate spectra and detecting climate change. Clim Chang 21:275–287CrossRefGoogle Scholar
  3. Chapman W, Walsh J (1993) Recent variation in sea ice and air temperature at high latitudes. BAMS 94:33–48CrossRefGoogle Scholar
  4. Diebold FX, Inoue A (2001) Long memory and regime switching. J Econ 105:131–159Google Scholar
  5. Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 13:253–263CrossRefGoogle Scholar
  6. 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 42:2417–2434Google Scholar
  7. Fomby T, Vogelsang T (2002) The application of size robust trend statistics to global warming temperature series. J Clim 15:117–123CrossRefGoogle Scholar
  8. Ghil M, Vautard R (1991) Interdecadal oscillations and the warming trend in global temperature time series. Nature 350:324–327CrossRefGoogle Scholar
  9. Gil-Alana LA (2002) Seasonal long memory in the aggregate output. Econ Lett 74:333–337CrossRefGoogle Scholar
  10. Gil-Alana LA (2003) An application of fractional integration to a long temperature time series. Int J Climatol 23:1699–1710CrossRefGoogle Scholar
  11. 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):429–436CrossRefGoogle Scholar
  12. Gil-Alana LA (2005) Statistical model of the temperatures in the northern hemisphere using fractional integration techniques. J Clim 18:5357–5369CrossRefGoogle Scholar
  13. Gil-Alana LA, Robinson PM (1997) Testing unit roots and other nonstationary hypotheses in macroeconomic time series. J Econ 80:241–268Google Scholar
  14. Gil-Alana LA, Robinson PM (2001) Testing of seasonal fractional integration in the UK and Japanese consumption and income. J Appl Econ 16:95–114CrossRefGoogle Scholar
  15. Granger CWJ (1980) Long memory relationships and the aggregation of dynamic models. J Econ 14:227–238Google Scholar
  16. Gray HL, Yhang N, Woodward WA (1989) On generalized fractional processes. J Time Anal 10:233–257CrossRefGoogle Scholar
  17. Gray HL, Yhang N, Woodward WA (1994) A correction: on generalized fractional processes. J Time Anal 15:561–562CrossRefGoogle Scholar
  18. Grenander U, Rosenblatt M (1957) Statistical analysis of stationary time series. Chelsea Publishing Company, New YorkGoogle Scholar
  19. Hamilton JD (1994) Time series analysis. Princeton University Press, Princeton, p 820Google Scholar
  20. Hansen J, Lebedeff S (1987) Global trends of measured surface air temperature. J Geophys Res 92:345–372CrossRefGoogle Scholar
  21. Hansen J, Lebedeff S (1988) Global surface air temperatures. Update through 1987. Geophys Lett 15:323–326CrossRefGoogle Scholar
  22. Hartmann B, Wendler G (2005) The significance of the 1976 Pacific climate shift in the climatology of Alaska. J Clim 18(4824):4839Google Scholar
  23. Harvey DI, Mills TC (2001) Modelling global temperature trends using cointegration and smooth transition. Stat Model 1:143–159CrossRefGoogle Scholar
  24. Harvey DI, Leybourne SJ, Newbold P (1997) Testing the equality of prediction mean squared errors. Int J Forecast 13:281–291CrossRefGoogle Scholar
  25. Hasselmann K (1993) Optimal fingerprints for the detection of time dependent climate change. J Clim 6:1957–1971CrossRefGoogle Scholar
  26. Jones PD, Raper SCB, Wigley TML (1986) Southern hemisphere surface air temperature variations: 1851–1984. J Clim Appl Meteorol 25(9):1213–1230CrossRefGoogle Scholar
  27. Jones PD, Osborn TJ, Briffa KR (1997) Estimating sampling errors in large scale temperature averages. J Clim 10:2548–2568CrossRefGoogle Scholar
  28. 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, USAGoogle Scholar
  29. 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, 176–191Google Scholar
  30. Karoly D, Wu Q (2005) Detection of regional surface temperature trends. J Clim 18:4337–4343CrossRefGoogle Scholar
  31. Kaufmann RK, Stern DI (2002) Cointegration analysis of hemispheric temperature relations. J Geophys Res 107:4012CrossRefGoogle Scholar
  32. 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 77:279–289CrossRefGoogle Scholar
  33. 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)
  34. 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 81:729–732CrossRefGoogle Scholar
  35. Lewis PAW, Ray BK (1997) Modelling long-range dependence, nonlinearity and periodic phenomena in sea surface temperatures using TSMARS. J Am Stat Assoc 92:881–893Google Scholar
  36. Liu B, Xu M, Henderson M (2004) Taking China's temperature: daily range, warming trends and regional variations. J Clim 17:4453–4462CrossRefGoogle Scholar
  37. Maraun D, Rust HW, Timmer H (2004) Tempting long-memory on the interpretation of DFA results. Nonlinear Process Geophys 11:495–503CrossRefGoogle Scholar
  38. Mills TC (2007) Time series modelling of two millennia of northern hemisphere temperatures. J Roy Stat Soc Series A 170:83–94Google Scholar
  39. Neerchal NK, Brunenmeister SL (1993) Estimation of trend. In Patil GP, Rao CR (eds) Chesapeake Bay Water Quality Data, Multivariate Environmental Statistics. 407–421Google Scholar
  40. 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 133–192Google Scholar
  41. North GR, Kim K-Y (1995a) Detection of forced climate signals. Part II. Simulation results. J Clim 6:409–417CrossRefGoogle Scholar
  42. North GR, Kim K-Y (1995b) Regional simulations of greenhouse warming including natural variability. Bull Am Meteorol Soc 76:2171–2178CrossRefGoogle Scholar
  43. North GR, Kim K-Y, Shen SP, Hardin JW (1995) Detection of forced climate signals. Part I. Filter theory. J Clim 6:401–408CrossRefGoogle Scholar
  44. Park RE, Mitchell BM (1980) Estimating the autocorrelated error model with trended data. J Econ 13:185–201Google Scholar
  45. Pelletier J, Turcotte D (1999) Self-affine time series II. Applications and models. Adv Geophys 40:91–166CrossRefGoogle Scholar
  46. Percival DB, Overland JE, Mofjeld HO (2001) Interpretation of North Pacific variability as a short- and long-memory process. J Clim 14:4545–4559CrossRefGoogle Scholar
  47. 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 151–167CrossRefGoogle Scholar
  48. Pethkar JS, Selvam AM (1997) Nonlinear dynamics and chaos. Applications for prediction of weather and climate. Proc. TROPMET 97, Bangalare, IndiaGoogle Scholar
  49. Porter-Hudak S (1990) An application of the seasonal fractionally differenced model to the monetary aggregate. J Am Stat Assoc 85:338–344Google Scholar
  50. Prais SJ, Winsten CB (1954) Trend estimators and serial correlation, Cowles Commission Monograph, no. 23. Yale University Press, New Haven, CTGoogle Scholar
  51. Robeson SM (2008) Trends in time-varying perceptiles of daily minimum and maximum temperature over North America. Geophys Res Lett 31:4Google Scholar
  52. Robinson PM (1978) Statistical inference for a random coefficient autoregressive model. Scand J Stat 5:163–168Google Scholar
  53. Robinson PM (1994) Efficient tests of nonstationary hypotheses. J Am Stat Assoc 89:1420–1437Google Scholar
  54. Schlesinger ME, Ramankutty N (1994) Low-frequency oscillation in the global climate system of period 65–70 years. Nature 367:723–727CrossRefGoogle Scholar
  55. 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 46:159–207CrossRefGoogle Scholar
  56. Smith RL (1993) Long-range dependence and global warming. Statistics for the Environment (ed. Barnett V, Turkman KF pub. J. Wiley), 141–161Google Scholar
  57. Stafford J, Wendler G, Curtis J (2000) Temperature and precipitation of Alaska: 50 year. Trend analysis. Theor Appl Climatol 67:33–44CrossRefGoogle Scholar
  58. Stern ID, Kaufmann RK (2000) Is there a global warming signal in hemispheric temperature series? Clim Chang 47:411–438CrossRefGoogle Scholar
  59. Woodward WA, Gray HL (1993) Global warming and the problem of testing for trend in time series data. J Clim 6:953–962CrossRefGoogle Scholar
  60. Woodward WA, Gray HL (1995) Selecting a model for detecting the presence of a trend. J Clim 8:1929–1937CrossRefGoogle Scholar
  61. Zheng X, Basher RE, Thompson CS (1997) Trend detection in regional-mean temperature series. Maximum, minimum, mean, diurnal range and SST. J Clim 10:317–326CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Faculty of EconomicsUniversity of NavarraPamplonaSpain

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