8.7 Seasonality

A series with a strong annual cycle violates the identical-distribution part of \(H_0\) before any trend is considered: January and July are not draws from the same distribution. The Hirsch–Slack seasonal Mann–Kendall test handles this by computing \(S\) separately within each season and summing: \[S' = \sum ^{g}_{k=1} S_k, \hspace {0.8cm} \operatorname {var}(S') = \sum ^{g}_{k=1}\operatorname {var}(S_k),\] comparisons being made only between like seasons in different years. The variances add because the seasonal statistics are treated as independent; where that is doubtful, a covariance term is required.

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