Islam, Mohammad; Heiny, Erik; Robles, Francisco; Ram, Trevor (Utah Valley University)
Faculty Advisor: Islam, Mohammad (Utah Valley University, Mathematics); Heiny, Erik (Utah Valley University, Mathematics)
In this project, we investigate two methods to detect trend in the time series data, of which one proposed method what we call it "ADM- Average Difference Method" gives the estimate of trend , and the other method what we call it "AMD-Absolute Max Difference" determines if there is any trend in the time series data. Both methods are applicable to linear and nonlinear time series data. We assess the quality of our proposed methods and compare our methods with nonparametric Mann-kendall test through Monte Carlo simulation by calculating the power of the tests. The power comparisons show that ADM- Average Difference Method performs better than Mann-Kendall test when there is no autocorrelation in the time series observations and non-monotonic autocorrelated series. However, absolute max difference method works well compared to Mann-Kendall test for detecting the trend when data are autocorrelated. Finally, we use our proposed method along with those in use to detect trend in two standard datasets -Alta Snowfall data and Nile river water flow data. ADM was able to detect trend in the Nile water flow data as did MK test, which is supported by the visual identification. On the other hand, AMD method failed to detect the trend in the Nile data. For Alta snowfall data, our proposed methods and MK test didn't find any trend over time as supported by visual inspection result.