Mann-Kendall Trend Test and Sen's Slope Estimation MATLAB Implementation

This MATLAB implementation provides source code for performing Mann-Kendall trend testing and Sen's slope estimation. The following sections detail how to utilize these algorithms for analyzing trends in time series data. First, understanding the fundamental principles of both methods is essential. The Mann-Kendall trend test is a non-parametric statistical hypothesis test that detects monotonic trends in time series data. The algorithm works by comparing all possible pairs of data points, calculating the number of concordant and discordant pairs to determine trend direction and statistical significance through standardized test statistics. Sen's slope estimation is a robust non-parametric method that calculates the median of slopes between all data point pairs, providing a resistant measure of trend magnitude that's unaffected by outliers. To implement these analyses, begin by importing your time series data into MATLAB and converting it into a vector format. The core implementation includes two main functions: one for the Mann-Kendall test that computes the S statistic, variance, and Z-score with automatic continuity correction, and another for Sen's slope that calculates pairwise slopes and returns the median slope with confidence intervals. After processing, you can visualize the results using MATLAB's plotting functions like plot() for time series display and trendline overlay, or create statistical plots showing confidence bounds and significance indicators. The code structure follows MATLAB best practices with input validation, vectorized operations for efficiency, and clear output formatting. Key algorithmic considerations include handling tied values in the Mann-Kendall test and efficient computation of pairwise differences for Sen's slope using matrix operations rather than nested loops. This implementation aims to support environmental data analysis, climate studies, and any research requiring robust trend detection. For questions regarding the implementation details or statistical interpretations, please feel free to contact me through the repository's issue tracking system.