Testing and improving type 1 error performance of Sen's innovative trend analysis method

Recent Sen innovative trend analysis method (Sen_ITA) has high graphical visual ability in addition to quantitative trend identification analysis aspects. However, it is important to determine critical trend values as to whether they are significant according to a certain statistical significance level. In order to achieve such a goal, a certain amount or average percentages (5%, 10%, and 20%), bootstraps, and variance correction methods are frequently used by the researchers as evident from the literature. These methods accept either approximate critical values or require the transformation of the time series to suit their assumption requirements. In this paper, Monte Carlo simulation studies are used to measure error rates (type 1) as suggestion for critical trend value determinations for the Sen_ITA method. Sen_ITA critical trend formula has been developed originally depending on type 1 error rate exceedance expectation. The improved method (ITA_R) as suggested in this paper provides successful results by comparing it with the classic Mann-Kendall (MK) method. Furthermore, the ITA_R and MK methods have been applied to the mean daily maximum temperature series from England. The resulting trend values are generally consistent with the MK method and show an upward trend in all regions of England and during all seasons.