OPTIMAL PIECEWISE REGRESSION-ANALYSIS AND ITS APPLICATION TO GEOMAGNETIC TIME-SERIES

The geomagnetic secular variation of declination at many observatories in Europe is approximately two straight lines, with a sudden and mark ed change in slope at around 1969, Different components of the field a t other observatories show a similar change at around the same time, a nd there are suggestions of the same phenomenon, commonly referred to as a geomagnetic impulse, having occurred at other epochs. Modelling o f geomagnetic observatory records has usually assumed that an impulse occurred, and specified its date, making the analysis somewhat subject ive. Here we present a new algorithm, using regression, which tests th e hypothesis of quadratic time dependence of the field over all possib le 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 vect or annual means of geomagnetic data from 119 observatories.