A nonlinear second-order autoregressive analysis of time varying signals leads to simple inhomogeneous linear algebraic equations. This method was applied to the analysis of three types of geophysical signals: the fluctuation of sea level at Venice (Italy), 'harmonic tremors' at Stromboli (Eolian Islands), and the earth's crustal motion at L'Aquila (Italy). For more regular motions (earth's crustal motion), linear and nonlinear methods give essentially equivalent results. Compared to the customary linear autoregressive method, our method more accurately predicts nonlinearities whenever there is a sudden increase of the signal amplitude, such as sea level fluctuations and seismic tremors.

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