Trend estimation from frequently observed data

[1] This paper concerns the analysis of data collected at a much higher frequency than is of interest for trend estimation. With particular reference to water quality data, the trend is represented by a smooth curve in a generalized additive model (GAM) which includes terms for flow and seasonal effects. The residuals in the GAM form a stationary process consisting of an unobserved highly correlated stochastic process and a measurement error. It is shown how standard GAM software can be applied to prewhitened data and the trend obtained by back transformation. The main conclusion is that the data should be reduced to seasonal (e.g., monthly) means. In particular, adjustment for flow effects to assess long-term trends should depend on the relationship derived from monthly rather than short-term fluctuations in flow. There is very limited benefit from recording data at high frequency. An application to daily electrical conductivity data over a period of 34 years is given. Flow adjustment for the trend is discussed in this context.