Skip to main content

2017 | OriginalPaper | Buchkapitel

3. Statistical Trend Tests

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

There are various classically established trend identification tests in the literature and their preliminary explanations are useful for further and innovative trend proposal understandings. In general these methodologies are divided into two groups as parametric and non-parametric approaches. Each group is explained with its proper assumptions, restrictions and mathematical formulations so as to give the reader appreciation of the fundamental concepts, which are useful in the assessment of any trend identification procedure. The regression analysis, which is the first main methodology for the description of the mathematical expression of any trend, is presented with a set of restrictive assumption exposition that are not taken into consideration in many publications throughout the world. It is recommended that in the application of any methodology the researcher should be aware of the assumptions, restrictions and difficulties that may be confronted in the trend identification application researches.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Chernoff, H., & Zacks, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time. Annals of Mathematical Statistics, 35, 999–1018.CrossRef Chernoff, H., & Zacks, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time. Annals of Mathematical Statistics, 35, 999–1018.CrossRef
Zurück zum Zitat Connover, W. J. (1971). Practical non-parametric statistics. New York: John Wiley and Sons. Connover, W. J. (1971). Practical non-parametric statistics. New York: John Wiley and Sons.
Zurück zum Zitat Craddock, J. M. (1979). Methods of comparing annual rainfall records for climatic purposes. Weather, 34, 332–346.CrossRef Craddock, J. M. (1979). Methods of comparing annual rainfall records for climatic purposes. Weather, 34, 332–346.CrossRef
Zurück zum Zitat Dickey D. A. (1991). A primer on co-integration with an application to money and income, Federal Reserve Bank of St. Louis, 58–78, Reprinted in Rao (1995). Dickey D. A. (1991). A primer on co-integration with an application to money and income, Federal Reserve Bank of St. Louis, 58–78, Reprinted in Rao (1995).
Zurück zum Zitat Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.
Zurück zum Zitat Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.CrossRef Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.CrossRef
Zurück zum Zitat Dickey, D. A., Dennis, W., Daniel, J., & Thornton, L. (1991). A primer on cointegration with an application to money and income, Federal Reserve Bank of St. Louis, 58–78, reprinted in Rao (1995). Dickey, D. A., Dennis, W., Daniel, J., & Thornton, L. (1991). A primer on cointegration with an application to money and income, Federal Reserve Bank of St. Louis, 58–78, reprinted in Rao (1995).
Zurück zum Zitat EPA. (1974). Guideline for the evaluation of air quality trends. Office of air quality planning and standards, U.S. Environmental Protection Agency. EPA. (1974). Guideline for the evaluation of air quality trends. Office of air quality planning and standards, U.S. Environmental Protection Agency.
Zurück zum Zitat Feller, W. (1968). An introduction to probability theory and its applications (3rd ed., Vol. I), John Wiley and Sons Co. Feller, W. (1968). An introduction to probability theory and its applications (3rd ed., Vol. I), John Wiley and Sons Co.
Zurück zum Zitat Gardner, L. A., Jr. (1969). On detecting changes in the mean of normal variates. Annals of Mathematical Statistics, 40, 116–126.CrossRef Gardner, L. A., Jr. (1969). On detecting changes in the mean of normal variates. Annals of Mathematical Statistics, 40, 116–126.CrossRef
Zurück zum Zitat Gilbert, R. O. (1987). Statistical methods for environmental pollution monitoring. New York: Van Nostrand Reinhold. Gilbert, R. O. (1987). Statistical methods for environmental pollution monitoring. New York: Van Nostrand Reinhold.
Zurück zum Zitat Gomide, F. L. S. (1978). Markovian inputs and the Hurst phenomenon. Journal of Hydrology, 37, 23–45.CrossRef Gomide, F. L. S. (1978). Markovian inputs and the Hurst phenomenon. Journal of Hydrology, 37, 23–45.CrossRef
Zurück zum Zitat Himmelblau, D. M. (1969). Process analysis by statistical methods. New York: John Wiley and Sons. Himmelblau, D. M. (1969). Process analysis by statistical methods. New York: John Wiley and Sons.
Zurück zum Zitat Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 70–808. Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 70–808.
Zurück zum Zitat Hurst, H. E. (1956). Methods of using long-term storage in reservoirs. Proceedings of the Institution of Civil Engineers, Part I, 519–542. Hurst, H. E. (1956). Methods of using long-term storage in reservoirs. Proceedings of the Institution of Civil Engineers, Part I, 519–542.
Zurück zum Zitat Kanji, G. K. (2001). 100 statistical tests. New Delhi: Sage Publication, 111”pp. Kanji, G. K. (2001). 100 statistical tests. New Delhi: Sage Publication, 111”pp.
Zurück zum Zitat Kendall, M. G. (1955). Rank correlation methods, Charles Griffin, London. Kendall, M. G. (1955). Rank correlation methods, Charles Griffin, London.
Zurück zum Zitat Kendall, M. G. (1973). Time series. London: Griffin. Kendall, M. G. (1973). Time series. London: Griffin.
Zurück zum Zitat Kendall, M. G. (1975). Rank correlation methods, 4th edition. Charles Griffin, London, U.K. Kendall, M. G. (1975). Rank correlation methods, 4th edition. Charles Griffin, London, U.K.
Zurück zum Zitat Kendall, M. G., & Stuart, A. (1952). The advanced theory of statistics. Vol. 1: Distribution theory. Griffin, London. Kendall, M. G., & Stuart, A. (1952). The advanced theory of statistics. Vol. 1: Distribution theory. Griffin, London.
Zurück zum Zitat Kendall, M. G., & Stuart, A. (1973). The advanced theory of statistics (Vol. II). New York: Hafner. Kendall, M. G., & Stuart, A. (1973). The advanced theory of statistics (Vol. II). New York: Hafner.
Zurück zum Zitat Khaliq, M. N., Ouarda, T. B. M. J., Gachon, P., Sushama, L., & StHilaire, A. (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. Journal of Hydrology, 368, 117–130. Khaliq, M. N., Ouarda, T. B. M. J., Gachon, P., Sushama, L., & StHilaire, A. (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. Journal of Hydrology, 368, 117–130.
Zurück zum Zitat Koçak, K., & Şen, Z. (1998). Applied examination of dry and wet day occurrences via markov chain approach. Turkish Journal of Engineering and Environmental Science, 22, 479–487. Koçak, K., & Şen, Z. (1998). Applied examination of dry and wet day occurrences via markov chain approach. Turkish Journal of Engineering and Environmental Science, 22, 479–487.
Zurück zum Zitat Kolaz, D. J., & Swinford, R. L. (1988). Ozone air quality: How does chicago rate? 81st annual meeting of the air pollution control association. Texas, USA: Dallas. Kolaz, D. J., & Swinford, R. L. (1988). Ozone air quality: How does chicago rate? 81st annual meeting of the air pollution control association. Texas, USA: Dallas.
Zurück zum Zitat Kolaz, D. J., & Swinford, R. L. (1989). Ozone trends in the greater chicago area. Ozone Conference on Federal Controls for Ozone Around Lake Michigan, Lake Michigan States’ Section and Wisconsin Chapter of the Air and Waste Management Association. Kolaz, D. J., & Swinford, R. L. (1989). Ozone trends in the greater chicago area. Ozone Conference on Federal Controls for Ozone Around Lake Michigan, Lake Michigan States’ Section and Wisconsin Chapter of the Air and Waste Management Association.
Zurück zum Zitat Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178 (North-Holland). Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178 (North-Holland).
Zurück zum Zitat Lettenmaier, D. P. (1976). Detection of trends in water quality data from records with dependent observations. Water Resources Research, 12(5), 1037–1046.CrossRef Lettenmaier, D. P. (1976). Detection of trends in water quality data from records with dependent observations. Water Resources Research, 12(5), 1037–1046.CrossRef
Zurück zum Zitat Mann, H. B. (1945). Nonparametric tests against trend. Econometrica, 13(3), 245–259.CrossRef Mann, H. B. (1945). Nonparametric tests against trend. Econometrica, 13(3), 245–259.CrossRef
Zurück zum Zitat Mills, T. C. (1993). The econometric modelling of financial time series. Cambridge: Cambridge University Press. Mills, T. C. (1993). The econometric modelling of financial time series. Cambridge: Cambridge University Press.
Zurück zum Zitat Montgomery, R. H., & Reckhow, K. H. (1984). Techniques for detecting trends in lake water quality. Water Resources Bulletin, 20(1), 43–52.CrossRef Montgomery, R. H., & Reckhow, K. H. (1984). Techniques for detecting trends in lake water quality. Water Resources Bulletin, 20(1), 43–52.CrossRef
Zurück zum Zitat Parzen, E. (1960). Modern probability theory and its applications. John Wiley & Sons, New York. Parzen, E. (1960). Modern probability theory and its applications. John Wiley & Sons, New York.
Zurück zum Zitat Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75, 335–346. Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75, 335–346.
Zurück zum Zitat Qwen, D. B. (1962). Handbook of srtatistical tables. Reading, Massachusetts, USA: Addison-Wesley. Qwen, D. B. (1962). Handbook of srtatistical tables. Reading, Massachusetts, USA: Addison-Wesley.
Zurück zum Zitat Rao, B. B. (1995). Cointegration for the applied economist. London: Macmillan. Rao, B. B. (1995). Cointegration for the applied economist. London: Macmillan.
Zurück zum Zitat Saldarriga, J., & Yevjevich, V. (1979). Application of run-lengths to hydrologic time series. Hydrology Paper 40. Colorado State University, Fort Collins, USA. Saldarriga, J., & Yevjevich, V. (1979). Application of run-lengths to hydrologic time series. Hydrology Paper 40. Colorado State University, Fort Collins, USA.
Zurück zum Zitat Searcy, J. K., & Hardison, H. H. (1960). Manual of hydrology: Part 1, general surface-water techniques double-mass curves. U.S. Geological Survey, Water Supply Paper 1541-B. Searcy, J. K., & Hardison, H. H. (1960). Manual of hydrology: Part 1, general surface-water techniques double-mass curves. U.S. Geological Survey, Water Supply Paper 1541-B.
Zurück zum Zitat Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall’s Tau. Journal of the American Statistical Association, 63(324), 1379–1389.CrossRef Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall’s Tau. Journal of the American Statistical Association, 63(324), 1379–1389.CrossRef
Zurück zum Zitat Şen, Z. (1974). Small sample properties of stationary stochastic processes and hurst phenomenon in hydrology. Unpublished Ph. D. Thesis, University of London, 256 pp. Şen, Z. (1974). Small sample properties of stationary stochastic processes and hurst phenomenon in hydrology. Unpublished Ph. D. Thesis, University of London, 256 pp.
Zurück zum Zitat Şen, Z. (1976). Wet and dry periods of annual flow series. Journal of the Hydraulics Division, 102, 1503–1514 (ASCE Proceedings of the Paper, 12497). Şen, Z. (1976). Wet and dry periods of annual flow series. Journal of the Hydraulics Division, 102, 1503–1514 (ASCE Proceedings of the Paper, 12497).
Zurück zum Zitat Şen, Z. (1978). Autorun analysis of hydrologic time series. Journal of Hydrology, 36, 75–85.CrossRef Şen, Z. (1978). Autorun analysis of hydrologic time series. Journal of Hydrology, 36, 75–85.CrossRef
Zurück zum Zitat Shahin, et al. (1993). In D. Machiwal & M. K. Jha. In hydrologic time series analysis: Theory and practice (p. 301). Springer Publisher. Shahin, et al. (1993). In D. Machiwal & M. K. Jha. In hydrologic time series analysis: Theory and practice (p. 301). Springer Publisher.
Zurück zum Zitat Sneyer, R. (1992). On the use of statistical analysis for the objective determination of climate change. Meteorologishe Zeitshrifft, N.F., 247–256. Sneyer, R. (1992). On the use of statistical analysis for the objective determination of climate change. Meteorologishe Zeitshrifft, N.F., 247–256.
Zurück zum Zitat Sonali, P. & Kumar, D. N. (2013). Review of trend detection methods and their application to detect temperature changes in India. Journal of Hydrology, 476, 212–227. Sonali, P. & Kumar, D. N. (2013). Review of trend detection methods and their application to detect temperature changes in India. Journal of Hydrology, 476, 212–227.
Zurück zum Zitat Sweitzer, T. A., & Kolaz, D. J. (1984). An assessment of the influence of meteorology on the trend of ozone concentrations in the chicago area. In Air Pollution Control Association Specialty Conference on “Quality Assurance in Air Pollution Measurements,” Boulder, Colorado, USA. Sweitzer, T. A., & Kolaz, D. J. (1984). An assessment of the influence of meteorology on the trend of ozone concentrations in the chicago area. In Air Pollution Control Association Specialty Conference on “Quality Assurance in Air Pollution Measurements,” Boulder, Colorado, USA.
Zurück zum Zitat Wallis, J. R., & O’Connell, P. E. (1973). Firm reservoir yield—How reliable are historic hydrological records? Hydrological Sciences Bulletin, 18, 347–365.CrossRef Wallis, J. R., & O’Connell, P. E. (1973). Firm reservoir yield—How reliable are historic hydrological records? Hydrological Sciences Bulletin, 18, 347–365.CrossRef
Zurück zum Zitat WMO (World Meteorological Organization). (1966). Climate change. Technical Note No. 79, WMO No. 195, TP 200, I-20, WM, Geneva, Switzerland. WMO (World Meteorological Organization). (1966). Climate change. Technical Note No. 79, WMO No. 195, TP 200, I-20, WM, Geneva, Switzerland.
Zurück zum Zitat Yevjevich, V. (1967). An objective approach to definition and investigation of continental hydrologic droughts. Hydrology Paper 23. Colorado State University, Fort Collins, USA. Yevjevich, V. (1967). An objective approach to definition and investigation of continental hydrologic droughts. Hydrology Paper 23. Colorado State University, Fort Collins, USA.
Zurück zum Zitat Yevjevich, V., & Jeng, R.J. (1969). Properties of non-homogeneous hydrologic series. Hydrolology Paper 32, Colo. State Univ., Fort Collins, USA. Yevjevich, V., & Jeng, R.J. (1969). Properties of non-homogeneous hydrologic series. Hydrolology Paper 32, Colo. State Univ., Fort Collins, USA.
Zurück zum Zitat Yue, S., & Wang, C. (2004). The Mann–Kendall test modified by effective sample size to detect trend in serially correlated hydrological series. Water Resource Manage, 18, 201–218. Yue, S., & Wang, C. (2004). The Mann–Kendall test modified by effective sample size to detect trend in serially correlated hydrological series. Water Resource Manage, 18, 201–218.
Zurück zum Zitat Yue, S., Pilon, P., & Phinney, B. (2004). Canadian streamflow trend detection: impacts of serial and cross-correlation. Hydrogical Sciences Journal, 48(1), 51-64. Yue, S., Pilon, P., & Phinney, B. (2004). Canadian streamflow trend detection: impacts of serial and cross-correlation. Hydrogical Sciences Journal, 48(1), 51-64.
Metadaten
Titel
Statistical Trend Tests
verfasst von
Zekâi Şen
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-52338-5_3