Context : One of the most unusual aspects of the X-ray binary LS I +61 ^ { \circ } 303 is that at each orbit ( P _ { 1 } = 26.4960 \pm 0.0028 d ) one radio outburst occurs whose amplitude is modulated with P _ { long } , a long-term period of more than 4 yr .
It is still not clear whether the compact object of the system or the companion Be star is responsible for the long-term modulation .

Aims : We study here the stability of P _ { long } .
Such a stability is expected if P _ { long } is due to periodic ( P _ { 2 } ) Doppler boosting of periodic ( P _ { 1 } ) ejections from the accreting compact object of the system .
On the contrary it is not expected if P _ { long } is related to variations in the mass loss of the companion Be star .

Methods : We built a database of 36.8 yr of radio observations of LS I +61 ^ { \circ } 303 covering more than 8 long-term cycles .
We performed timing and correlation analysis .
We also compared the results of the analyses with the theoretical predictions for a synchrotron emitting precessing ( P _ { 2 } ) jet periodically ( P _ { 1 } ) refilled with relativistic electrons .

Results : In addition to the two dominant features at P _ { 1 } and P _ { 2 } , the timing analysis gives a feature at P _ { long } = 1628 \pm 48 days .
The determined value of P _ { long } agrees with the beat of the two dominant features , i.e . P _ { beat } = 1 / ( \nu _ { 1 } - \nu _ { 2 } ) = 1626 \pm 68 d. Lomb-Scargle results of radio data and model data compare very well .
The correlation coefficient of the radio data oscillates at multiples of P _ { beat } , as does the correlation coefficient of the model data .

Conclusions : Cycles in varying Be stars change in length and disappear after 2-3 cycles following the well-studied case of the binary system \zeta Tau .
On the contrary , in LS I +61 ^ { \circ } 303 the long-term period is quite stable and repeats itself over the available 8 cycles .
The long-term modulation in LS I +61 ^ { \circ } 303 accurately reflects the beat of periodical Doppler boosting ( induced by precession ) with the periodicity of the ejecta .
The peak of the long-term modulation occurs at the coincidence of the maximum number of ejected particles with the maximum Doppler boosting of their emission ; this coincidence occurs every \frac { 1 } { \nu _ { 1 } - \nu _ { 2 } } and creates the long-term modulation observed in LS I +61 ^ { \circ } 303 .