## 1 Introduction

[2] The first time derivative of the geomagnetic field, i.e., the secular variation (SV), represents the temporal evolution of the Earth's core magnetic field. The most rapid features in the changes of slopes of this magnetic secular variation are the so-called *geomagnetic jerks* [*Courtillot et al*., 1978] or as recently suggested, *geomagnetic rapid secular fluctuations* [*Olsen and Mandea*, 2008; *Mandea and Olsen*, 2009], which have time scales from several months to a few years [*Macmillan*, 2007]. These events are observed in magnetic data as sudden V-shaped changes in the slope of SV, in other words, as an abrupt change in the second time derivative, i.e., the secular acceleration series, or equivalently, as a Dirac-delta function in the third time derivative [*Mandea et al*., 2010]. Usually, geomagnetic jerks are particularly visible in the eastward (Y) component, which is supposed to be the less affected by external fields.

[3] In the past, different types of analysis have been introduced to allow the identification of geomagnetic jerks. Methods of detection of geomagnetic jerks are various, mostly based on spectral techniques [e.g., *Mandea et al*., 2010, and references therein], or techniques applied mostly to direct magnetic measurements or global geomagnetic models [e.g., *Chambodut and Mandea*, 2005]. We propose here a new method that is not a spectral one, because it is based on the so-called nonlinear forecasting approach [NFA; *Sugihara and May*, 1990]. This technique is able to detect a possible exponential divergence of some prediction from the real signal in the phase space, which is reconstructed from the time delay of the original signal. An important parameter is the mean exponential characteristic time τ, after which no reliable prediction can be made [*Barraclough and De Santis*, 1997; *De Santis et al*., 2002].

[4] Combining this technique with the most classical and widely used in geomagnetism, i.e., the spherical harmonic analysis, we can perform our analysis in the usual time domain by taking advantage of the geomagnetic field ergodicity [*De Santis et al*., 2011]. This study deals with the detection and, possibly, confirmation of the presence of geomagnetic jerks by means of NFA in time, to find those epochs when the geomagnetic field appears more chaotic, i.e., those less predictable periods that are characterized by smaller characteristic time τ. We then consider these epochs as possible estimates of jerk occurrence dates.

[5] The organization of this paper is as follows. After this introduction, section 2 describes more in detail the geomagnetic jerk phenomena. Section 3 is dedicated to the nonlinear chaotic analysis of the geomagnetic field, followed by section 4, where the global geomagnetic model used for this analysis is introduced. In section 5 we describe the NFA in the time domain whereas section 6 shows the temporal behavior of errors between predicted and actual geomagnetic models: the trend in time of these errors is used to detect geomagnetic jerks. Finally, we discuss the results in section 7.