OPTIMAL PIECEWISE REGRESSION ANALYSIS AND ITS APPLICATION TO GEOMAGNETIC TIME SERIES

SUMMARY The geomagnetic secular variation of declination at many observatories in Europe is approximately two straight lines, with a sudden and marked change in slope at around 1969. Different components of the field at other observatories show a similar change at around the same time, and there are suggestions of the same phenomenon, commonly referred to as a geomagnetic impulse, having occurred at other epochs. Modelling of geomagnetic observatory records has usually assumed that an impulse occurred, and specified its date, making the analysis somewhat subjective. Here we present a new algorithm, using regression, which tests the hypothesis of quadratic time dependence of the field over all possible time intervals, ranking them such that the data series are modelled by the fewest such quadratics (i.e. the smallest number of parameters) that provide an adequate fit to the data. In this way, the dates of any impulses are determined objectively, rather than imposed a priori, and the adequacy of quadratic time dependence is assessed. The method is tested on synthetic data, and then applied to a total of 5766 vector annual means of geomagnetic data from 119 observatories.