8 Non-Parametric Methods for Trend
Everything so far has compared groups. This chapter asks a different question: does a single series measured through time drift steadily up or down? The question matters in hydrology, climate, water quality, epidemiology and economics, and it is one where the non-parametric answer has largely displaced the parametric one in practice.
Ordinary least-squares regression on time will answer it, but only under assumptions that environmental series routinely break: normal errors, constant variance, no outliers, and a trend that is genuinely straight. The methods below assume only that the observations are independent and that the trend, if any, is monotonic — consistently in one direction, not necessarily linear. That is a much weaker requirement, and it buys robustness to outliers and to skewness, both of which rainfall and streamflow have in abundance.
8.2 The Variance of \(S\), With Ties
8.3 The Theil–Sen Slope
8.4 Serial Correlation, and Why It Breaks the Test
8.5 A Warning Not Found in the Textbooks
8.6 Testing Many Series at Once
8.7 Seasonality
8.8 Practice Problems
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