The Fast Fourier Transform (FFT) as a statistical tool for time-series analysis

Many geosciences phenomena show cyclic/periodic behaviour, or can show this under certain conditions, e.g. soil gas concentrations/emissions, earthquakes, droughts and floods, whereas others are anomalous, recurring apparently randomly with regard to time, e.g. earthquakes and volcanic eruptions (under most circumstances). For the cyclic cases, an analysis of past time-series can yield an expectation and perhaps some degree of forecasting, even if only at the level of 'more probable' and 'less probable' times of occurrence. The aim of this short-course is to provide an introduction to and overview of the Discrete/Fast Fourier Transform as a key underpinning technique of time-series analysis to identify and quantify periodic features, as distinct from its more conventional usage in digitisation and signal-analysis. The session will take the key question "Are we looking for cyclic or anomalous phenomena?" as its starting point and will focus on the application of the Fast Fourier Transform, as implemented in many software packages, and interpretation of the output, including assessment of statistical effectsize. It will conclude with an introduction to periodgram approaches for unequal-interval timeseries.