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The high-mass X-ray binary LS I +61$^\circ$303 is detected across theelectromagnetic spectrum from radio until the very high energy gamma-rayregime. The emission is not only highly variable on many time scales, but isalso periodic at all observed wavelengths. Periodic modulation was observed ondifferent time-scales, ranging from hours, over months to several years. Thesubject of this article is a super-orbital, long-term modulation of ~4.6 years.We review the observation of this periodic modulation at multiple wavelengthsand investigate systematic relationships between them. In particular, radioobservations reveal that the long-term modulation is a very stable feature ofthe source. Observations at other wavelengths result in a phase-shift of themodulation pattern that is a systematic function of energy. The stability ofthis period favors a scenario in which the long-term modulation is the resultof a precessing jet giving rise to periodic changes in the Doppler factor,beating with the orbital modulation of the accretion rate. We explain thephase-shifts across energy bands in a scenario with shorter wavelengthsoriginating closer to the base of the presessing jet. A significant deviationof the TeV emission from this trend possibly requires a different explanationrelated to magnetic reconnection events.

A Precessing Jet Scenario for the Multi-Wavelength Long-Term Modulation of LS I +61$^\circ$303