Our paper is dedicated to the problem of anomalous values of braking indices nobs and spin frequency second derivatives \documentclass[12pt]{minimal}
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\begin{document}$$\ddot \nu$$\end{document} of isolated radio pulsars. Observations of these objects for over 40 years have shown that in addition to the complex short-term irregular component in the evolution of the pulsars’ frequency, secular values of its second derivative are orders of magnitude greater than the predicted theoretical ones, and in a good half of cases—they are even negative. We earlier attributed this behavior of secular values of the second derivative to the presence of a cyclic component in the secular evolution of ν(t), with a characteristic recurrence time of thousands to tens of thousand years. We continue to develop this hypothesis based on a more detailed statistical analysis of the characteristics of 297 isolated radio pulsars: we analyze the model of these objects spin-down, consisting of two components, monotonic and cyclic, and determine their parameters. We demonstrate that the monotonic spin-down component is described by the classical magnetodipolar power law with an braking index of about 3, while the large amplitude of the cyclic component causes a significant variation of the observed spin-down rate \documentclass[12pt]{minimal}
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\begin{document}$$(\dot \nu )$$\end{document} (with respect to magnetodipolar one), and fully determines the anomalous values of \documentclass[12pt]{minimal}
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\begin{document}$$\ddot \nu$$\end{document} and nobs. An important consequence of the existence of a cyclic component of the pulsar rotational variations is the difference between their characteristic ages and respective secular values (by about 0.5–5 times). This allows to explainthe observed discrepancy of the characteristic and physical ages of some objects, as well as very large, up to 108 years, characteristic ages of some old pulsars. The paper argues that the cyclic component of the observed spin-down is due to the long-term precession of neutron stars around their magnetic axes, which, in particular, may be driven by the anomalous braking torque. In the model of purely magnetodipolar braking this torque is a consequence of emission in the near field zone.
