**5.5 Applying these UR tests**

Assuming an objective change-point method has been used bounded between two objectively determined change-points. Do the assumptions of the detection method hold for the segment of data and to what extent?

These tests are all applied to the segments of data within which a single changepoint has already been provisionally identified. The change-point itself is not otherwise considered. However, since the climate data being tested provisionally contains a deterministic change and only the ZA test is formulated with this as a ruling assumption, findings of non-stationarity may be caused by the presence of additional deterministic change-points below detection thresholds.

Level stationarity is not simply a zero trend, since data with zero trend may be either deterministically or stochastically level, and even if deterministic may not be linear. A deterministic change-point detection method may return indeterminate change-points given non-linear trend. The residuals around stochastic trend will retain a UR characteristic. Trend stationary data has level stationary residuals, as do discontinuous trend stationary data fitted appropriately.

A segment of data with a valid change point should not be found to be level stationary, it should not be in a segment with unit root behaviour, and if it shows trending behaviour this should not be due to a drifting unit root. It should also have low *p*-values by ANCOVA.
