Two Non-Parametric Trend Tests Applicable for Long-Memory Processes (Case Study: Mashhad Air Temperature)

Document Type : Original Article

Author

Professor of Irrigation, College of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

Trend investigation is one of the key characteristics of time series. However, all common trend tests (e,g. Kendall and Mann-Kendall) are based on stationary time series and with this assumption that there is no long-memory in the time series. Based on both classical Kendall and Mann-Kendall tests, it was shown in this study that there was a significant (p-value<0.001) increase in annual Mashhad temperature (with a record length of 127 years spanning 1885-2011). However, considering the time series as a long-memory process (fractional Gaussian normal with Hurst exponent of 0.92), standard deviation of the test statistics were increased by a factor of greater than 6. As a result, the increasing trend in temperature was not accepted at common significant levels of 0.01 and 0.05. Some regression equations were developed for correction of standard deviations of Kendall and Mann-Kendall trend tests as a function of record length and Hurst exponent, for the first time. The results remained identical for incomplete time series. A stochastic method, based on frequency factor of Chow, was proposed for data filling and showed that the results are stable.

Keywords

References

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Iran-Water Resources Research
Volume 9, Issue 3
February 2014
Pages 14-23

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History

  • Receive Date: 13 October 2012
  • Accept Date: 07 July 2013

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