Abstract
Trend identification procedures are employed to determine the systematic monotonic trend lines in a given hydro-meteorological time series records for depiction of time dependent changes in the form of increase or decrease. Different methodologies are proposed for such identifications, but most of them require restrictive assumptions such as the normal (Gaussian) probability distribution, serial independence and long sample sizes. In order to relieve especially the serial independence requirement pre-whitening and over-whitening procedures are suggested, but they cannot render a serially dependent series into completely independent structure. In this paper, a new trend methodology is proposed on the basis of crossing features along any given straight-line within the given time series and the one with the maximum crossing number is the searched trend component. This approach does not require any restrictive assumption. Contrary to the previous trend algorithms, the suggested crossing empirical trend analysis (CETA) yields not a single trend, but a set of trends at different levels within the variation range of hydro-meteorological time series records. In this paper for the sake of brevity only three levels are considered at 10%, 50% and 90% risk levels. The comparison of the CETA approach is presented with the classical and frequently used method of Mann-Kendall (MK) trend identification procedure based on the Sen’s slope calculation. For small serial correlation coefficients and normal probability distribution (PDF) function cases CETA and classical technique yield almost the same trend line within +5% error band limits. The application of this methodology is presented for monthly and annual discharge records of Danube River and annual precipitation records from seven geographical regions of Turkey.
Universal codes as a basis for nonparametric testing of serial independence for time series