This paper proposes an effective internal dynamic trend analysis method based on the mean and standard deviation as variability trends, providing additional information about the tendency of fluctuations around mean values. The novel method, called Structural Trend and Variability Identification (STVI), can identify a range of trends over different time periods in a given time series. To illustrate the proposed methodology, classical linear trends in the mean values and standard deviations (variability) for 10-year and 30-year identifications are given as examples, based on lag-shifting mechanism. A rea-world application of the STVI approach is given for annual Danube River discharge measurements over 160-year period from 1850 to 2010. Cumulative distribution functions (CDF) of trend slopes fitting Weibull and Pearson’s theoretical probability distribution function (PDF) are presented. CDFs offer opportunities for trend slope risks based on a range of return periods such as 2-year, 5-year, 10-year, 25-year and 50-year.
Zekai Şen (Wed,) studied this question.