Deterministic versus stochastic trends: Detection and challenges

Journal of Geophysical Research Atmospheres

Volumn 114, Issue 18, 2009, Pages

  Fatichi, S ^a   Barbosa, S M ^b   Caporali, E ^a   Silva, M E ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; HEURISTIC METHODS; STATISTICAL TESTS; STOCHASTIC SYSTEMS; TIME SERIES; WAVELET ANALYSIS;

AVERAGE TEMPERATURE; FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING AVERAGE MODELS; GEOPHYSICAL RESEARCHES; LOCAL SCALE; LONG RANGE DEPENDENCE; LONG-TERM CLIMATE VARIABILITY; MANN-KENDALL; NON-PARAMETRIC; PHILLIPS; STATIONARY BEHAVIOR; STATISTICAL SIGNIFICANCE; STOCHASTIC BEHAVIOR; STOCHASTIC TRENDS; TREND DETECTION; TUSCANY;

CLIMATE CHANGE;

CLIMATE CHANGE; CLIMATE VARIATION; GEOPHYSICAL SURVEY; HEURISTICS; STATISTICAL ANALYSIS; STOCHASTICITY; TIME SERIES; WAVELET ANALYSIS;

EURASIA; EUROPE; ITALY; SOUTHERN EUROPE; TUSCANY;

EID: 72049125637     PISSN: 01480227     EISSN: None     Source Type: Journal    
DOI: 10.1029/2009JD011960     Document Type: Article

References (82)

1. Abry, P., P. Flandrin, M. S. Taqqu, and D. Veitch (2003), Self-similarity and long range dependence through the wavelet lens, in Theory and Applications of Long Range Dependence, edited by O. G. Doukhan and M. S. Taqqu, pp. 527-556, Birkhuser, Basel.
2. Barbosa, S. M., M. J. Fernandes, and M. E. Silva (2006a), Long range dependence in North Atlantic sea level, Physica A, 371, 725-731.
3. Barbosa, S. M., M. E. Silva, and M. J. Fernandes (2006b), Wavelet analysis of the Lisbon and Gibraltar North Atlantic Oscillation winter indices, Int. J. Climatol., 26, 581-593.
4. Barbosa, S. M., M. E. Silva, and M. J. Fernandes (2008), Time series analysis of sea-level records: Characterising long-term variability, in Nonlinear Time Series Analysis in the Geosciences - Applications in Climatology, Geodynamics, and Solar-Terrestrial Physics, edited by R. V. Donner and S. M. Barbosa, pp. 157-173, Springer, Berlin.
5. Benjamini, Y., and D. Yekutieli (2001), The control of the false discovery rate in multiple testing under dependency, Ann. Stat., 29(4), 1165-1188. (Pubitemid 33575263)
6. Beran, J. (1994), Statistic for Long-Memory Processes, Chapman and Hall, New York.
7. Bras, R. L., and I. Rodriguez-Iturbe (1994), Random Function and Hydrology, vol.21, Dover, New York.
8. Brunetti, M., M. Colacino, M. Maugeri, and T. Nanni (2001), Trends in the daily intensity of precipitation in Italy from 1951 to 1996, Int. J. Climatol., 21, 299-316. (Pubitemid 32292265)
9. Buhlmann, P. (2002), Bootstrap for time series, Stat. Sci., 17(1), 52-72.
10. Burn, D., A. Mohamed, and H. Elnur (2002), Detection of hydrologic trends and variability, J. Hydrol., 255, 107-122.
11. Caballero, R., S. Jewson, and A. Brix (2002), Long memory in surface air temperature: Detection, modeling, and application to weather derivative valuation, Clim. Res., 21, 127-140.
12. Cairncross, A. (1971), Essays in Economic Management, Allen and Unwin, London.
13. Cleveland, R. B., W. S. Cleveland, J. E. McRae, and I. Terpenning (1990), STL: A seasonal-trend decomposition procedure based on loess, J. Off. Stat., 6, 3-73.
14. Cohn, T. A., and H. F. Lins (2005), Nature's style: Naturally trendy, Geophys. Res. Lett., 32, L23402, doi:10.1029/2005GL024476.
15. Conover, W. J. (1999), Practical Nonparametric Statistics, 3rd ed., John Wiley, New York.
16. Cox, D. R., and A. Stuart (1955), Some quick tests for trend in location and dispersion, Biometrika, 42, 80-95.
17. Daniels, H. E. (1950), Rank correlation and population models, J. R. Stat. Soc. Ser. B, 12, 171-181.
18. Davison, A. C., and D. V. Hinkley (1997), Bootstrap Methods and Their Application, Cambridge Univ. Press, New York.
19. Diebolt, C., and V. Guiraud (2005), A note on long memory time series, Qual. Quant., 39, 827-836, doi:10.1007/s11135-004-0436-z. (Pubitemid 41426172)
20. Doukhan, P., G. Oppenheim, and M. S. Taqqu (2003), Theory and Applications of Long-Range Dependence, Birkhuser, Basel.
21. Franco, G. C., and V. A. Reisen (2004), Bootstrap techniques in semiparametric estimation methods for ARFIMA models: A comparison study, Comput. Stat., 19, 243-259.
22. Franco, G. C., and V. A. Reisen (2007), Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes, Physica A, 375, 546-562, doi:10.1016/j.physa.2006.08.027.
23. Geweke, J., and S. Porter-Hudak (1983), The estimation and application of long memory time series models, J. Time Ser. Anal., 4, 221-238.
24. Granger, C.W. J., and R. Joyeux (1980), An introduction to long-range time series models and fractional differencing, J. Time Ser. Anal., 1, 15-30.
25. Grimaldi, S. (2004), Linear parametric models applied to daily hydrological series, J. Hydrol. Eng., 9(5), 383-391.
26. Groisman, P. Y., R.W. Knight, T. R. Karl, D. R. Easterling, B. Sun, and J. H. Lawrimore (2004), Contemporary changes of the hydrological cycle over the contiguous United States: Trends derived from in situ observations, J. Hydrometeorol., 5(1), 64-85.
27. Hamed, K. H. (2008), Trend detection in hydrologic data: The Mann- Kendall trend test under scaling hypothesis, J. Hydrol., 349, 350-363, doi:10.1016/j.jhydrol.2007.11.009.
28. Hamed, K. H., and A. R. Rao (1998), A modified Mann-Kendall trend test for autocorrelated data, J. Hydrol., 204, 182-196.
29. Härdle, W., J. Horowit, and J.-P. Kreiss (2003), Bootstrap methods for time series, Int. Stat. Rev., 71(2), 435-459.
30. Haslett, J., and A. E. Raftery (1989), Space-time modelling with long-memory dependence: Assessing Ireland's wind power resource (with discussion), Appl. Stat., 38(1), 1-50.
31. Hosking, J. R. M. (1981), Fractional differencing, Biometrika, 68, 165-176.
32. Hu, K., I. P. Ch., Z. Chen, P. Carpena, and H. E. Stanley (2001), Effects of trends on detrended fluctuation analysis, Phys. Rev. E, 64, 011114, doi:10.1103/PhysRevE.64.011114.
33. Hurst, H. E. (1951), Long-term storage capacity of reservoirs, Trans. Am. Soc. Civ. Eng., 116, 770-779.
34. Intergovernmental Panel on Climate Change (IPCC) (2007), Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge Univ. Press, New York.
35. Jach, A., and P. Kokoszka (2008), Wavelet-domain test for long-range dependence in the presence of a trend, Statistics, 42, 101-113.
36. Kallache, M., H. W. Rust, and J. Kropp (2005), Trend assessment: Applications for hydrology and climate research, Nonlinear Process. Geophys., 12, 201-210. (Pubitemid 40367828)
37. Kendall, M. G. (1975), Rank Correlation Methods, Griffin, London.
38. Khaliq,M. N., T. B. M. J. Ouarda, P. Gachon, L. Sushama, and A. St-Hilaire (2009), Identification of hydrological trends in the presence of serial and cross correlations: A review of selected methods and their application to annual flow regimes of Canadian rivers, J. Hydrol., 368, 117-130, doi:10.1016/j.jhydrol.2009.01.035.
39. Kiràly, A., and I. M. Janosi (2005), Detrended fluctuation analysis of daily temperature records: Geographic dependence over Australia, Meteorol. Atmos. Phys., 88, 119-128. (Pubitemid 40594917)
40. Klemeš, V. (1974), The Hurst phenomenon - A puzzle?, Water Resour. Res., 10, 675-688.
41. Koscielny-Bunde, E., J. W. Kantelhardt, P. Braun, A. Bunde, and S. Havlin (2006), Long-term persistence and multifractality of river runoff records: Detrended fluctuations studies, J. Hydrol., 322, 120-137.
42. Koutsoyiannis, D. (2002), The Hurst phenomenon and fractional Gaussian noise made easy, Hydrol. Sci. J., 47(4), 573-595.
43. Koutsoyiannis, D. (2003), Climate change, the Hurst phenomenon and hydrological statistics, Hydrol. Sci. J., 48(1), 3-24.
44. Koutsoyiannis, D. (2005), Uncertainty, entropy, scaling and hydrological sthochastics, 2. Time dependence of hydrological processes, Hydrol. Sci. J., 50(43), 405-426.
45. Koutsoyiannis, D. (2006), Nonstationarity versus scaling in hydrology, J. Hydrol., 324, 239-254, doi:10.1016/j.jhydrol.2005.09.022.
46. Koutsoyiannis, D., and A. Montanari (2007), Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resour. Res., 43, W05429, doi:10.1029/2006WR005592. (Pubitemid 46998230)
47. Kwiatkowski, D., P. Phillips, P. Schmidt, and Y. Shin (1992), Testing the null hypothesis of stationarity against the alternative of a unit root, J. Econometrics, 159-178.
48. Lettenmaier, D. P., E. F.Wood, and J. R.Wallis (1994), Hydro-climatological trends in the continental United States, 1948-88, J. Clim., 7, 586-607.
49. Ljung, L. (1999), System Identification: Theory for the User, Prentice-Hall, Upper Saddle River, N. J.
50. Mandelbrot, B. B., and J. W. V. Ness (1968), Fractional Brownian motions, fractional noises and application, Soc. Ind. Appl. Math. Rev., 10, 422-437.
51. Mann, H. B. (1945), Nonparametric tests against trend, Econometrica, 13, 245-259.
52. Mann, M. E., R. S. Bradley, and M. K. Hughes (1999), Northern Hemisphere temperatures during the past millennium: Inferences, uncertainties and limitations, Geophys. Res. Lett., 26(6), 759-762.
53. Maraun, D., H. Rust, and J. Timmer (2004), Tempting long memory - On the interpretation of DFA results, Nonlinear Process. Geophys., 11, 495-503. (Pubitemid 39660861)
54. McIntyre, S., and R. McKitrick (2003), Corrections to the Mann et al. (1998) proxy data base and Northern Hemispheric average temperature series, Energy Environ., 14(6), 751-771.
55. Moberg, A., D. M. Sonechkin, K. Holmgren, N. M. Datsenko, andW. Karlen (2005), Highly variable Northern Hemisphere temperatures reconstructed from low and high resolution proxy data, Nature, 433(7026), 613-617. (Pubitemid 40282990)
56. Montanari, A., and E. Toth (2007), Calibration of hydrological models in the spectral domain: An opportunity for scarcely gauged basins?, Water Resour. Res., 43, W05434, doi:10.1029/2006WR005184. (Pubitemid 46998235)
57. Montanari, A., R. Rosso, and M. S. Taqqu (1997), Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation and simulation, Water Resour. Res., 33(5), 1035-1044.
58. Montanari, A., R. Rosso, and M. S. Taqqu (2000), A seasonal fractional ARIMA model applied to the Nile river monthly flows at Aswan, Water Resour. Res., 36(5), 1249-1265. (Pubitemid 30254884)
59. Mudelsee, M. (2007), Long memory of rivers from spatial aggragation, Water Resour. Res., 43, W01202, doi:10.1029/2006WR005721.
60. Percival, D., and A. T. Walden (2000), Wavelet Methods for Time Series Analysis, Cambridge Univ. Press, New York.
61. Percival, D. B. (1995), On the estimation of the wavelet variance, Biometrika, 82, 619-631.
62. Percival, D. B. (2008), Analysis of geophysical time series using discrete wavelet transforms: An overview, in Nonlinear Time Series Analysis in the Geosciences - Applications in Climatology, Geodynamics, and Solar- Terrestrial Physics, edited by R. V. Donner and S. M. Barbosa, pp. 61-79, Berlin, Springer.
63. Phillips, P. C. B., and P. Perron (1988), Testing for a unit root in time series regression, Biometrika, 75, 335-346.
64. Reisen, V. A. (1994), Estimation of the fractional differential parameter in the ARIMA (p, d, q) model using the smoothed periodogram, J. Time Ser. Anal., 15(3), 335-350.
65. Robinson, P. M. (2003), Time Series With Long Memory, Advanced Texts in Econometrics, Oxford Univ. Press, New York.
66. Rust, H. W., O. Mestre, and V. K. C. Venema (2008), Fewer jumps, less memory: Homogenized temperature records and long memory, J. Geophys. Res., 113, D19110, doi:10.1029/2008JD009919.
67. Rybski, D., A. Bunde, S. Havlin, and H. von Storch (2006), Long-term persistence in climate and the detection problem, Geophys. Res. Lett., 33, L06718, doi:10.1029/2005GL025591.
68. Sibbertsen, P. (2003), Log-periodogram estimation of the memory parameter of a long-memory process under trend, Stat. Prob. Lett., 61(3), 261-268.
69. Silva, E. M., G. C. Franco, V. A. Reisen, and F. R. B. Cruz (2006), Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models, Computat. Stat. Data Anal., 51, 1002-1011, doi:10.1016/j.csda.2005.10. 007.
70. Stephenson, D. B., V. Pavan, and R. Bojariu (2000), Is the North Atlantic Oscillation a random walk?, Int. J. Climatol., 20, 1-18. (Pubitemid 30149928)
71. Syroka, J., and R. Toumi (2001), Scaling and persistence in observed and modeled surface temperature, Geophys. Res. Lett., 28, 3255-3258. (Pubitemid 32931862)
72. Taqqu, M. S., and V. Teverovsky (1997), Estimating long-range dependence in finite and infinite variance series, in A Practical Guide to Heavy Tails: Statistical Techniques for Analyzing Heavy Tailed Distributions, edited by R. F. R. Adler and M. S. Taqqu, Birkhuser, Boston, Mass.
73. Taqqu, M. S., V. Teverovsky, and W. Willinger (1995), Estimators for longrange dependence: An empirical study, Fractals, 3(4), 785-798.
74. Trenberth, K. E., et al. (2007), Observations: Surface and atmospheric climate change, in Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, chap. 3, Cambridge Univ. Press, New York.
75. Ventura, V., C. J. Paciorek, and J. S. Risbey (2004), Controlling the proportion of falsely rejected hypothesis when conducting multiple tests with climatological data, J. Clim., 17, 4343-4356. (Pubitemid 40047001)
76. Vyushin, D. I., and P. J. Kushner (2009), Power-law and long-memory characteristics of the atmospheric general circulation, J. Clim., doi:10.1175/2008JCLI2528.1, in press.
77. Wang, W., P. H. A. J. M. V. Gelder, J. K. Vrijling, and X. Chen (2007), Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes, Hydrol. Earth Syst. Sci., 11, 851-862. (Pubitemid 46226149)
78. Whittle, P. (1953), Estimation and information in stationarity time series, Ark. Mat., 2, 423-434.
79. Yue, S., and C. Y. Wang (2002), The applicability of pre-whitening to eliminate the influence of serial correlation on the Mann-Kendall test, Water Resour. Res., 38(6), 1068, doi:10.1029/2001WR000861.
80. Yue, S., and C. Y. Wang (2004), The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series, Water Resour. Manage., 18, 201-218. (Pubitemid 39306214)
81. Yue, S., P. Pilon, and G. Cavadias (2002a), Power of the Mann-Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series, J. Hydrol., 259, 254-271. (Pubitemid 34175777)
82. Yue, S., P. Pilon, B. Phinney, and G. Cavadias (2002b), The influence of autocorrelation on the ability to detect trend in hydrological series, Hydrol. Processes, 16, 1807-1829. (Pubitemid 34749913)