Estimation and detection of flexible trends

Literature on the estimation and detection of linear trends in (environmental) time series is extensive, as overviewed by Hess and others in work published in 2001. However, not all data patterns behave in a linear fashion or, at least, a monotonous increasing or decreasing fashion. Therefore, it may be advantageous to analyse data with more flexible trends. Once flexibility is introduced the problem of detecting statistically significant increase/decrease becomes much more complicated: the trend may be alternating between being constant, decreasing or increasing. As a consequence, the problem of detecting significant increases or decreases cannot be summarised in one single figure or statistical test, as in the case of linear trend detection.