Context : The gamma-ray binary LS I +61 ^ { \circ } 303 is a well-established source from centimeter radio up to very high energy ( VHE ; E > 100 GeV ) .
The broadband emission shows a periodicity of \sim 26.5 days , coincident with the orbital period .
A longer ( super-orbital ) period of 1667 \pm 8 days was proposed from radio variability and confirmed using optical and high-energy ( HE ; E ¿ 100 MeV ) gamma-ray observations .
In this paper , we report on a four-year campaign performed by MAGIC together with archival data concentrating on a search for a long-timescale signature in the VHE emission from LS I +61 ^ { \circ } 303 .

Aims : We focus on the search for super-orbital modulation of the VHE emission , similar to that observed at other energies , and on the search for correlations between TeV emission and an optical determination of the extension of the circumstellar disk .

Methods : A four-year campaign has been carried out using the MAGIC telescopes .
The source was observed during the orbital phases when the periodic VHE outbursts have occurred ( \phi = 0.55 – 0.75 , one orbit = 26.496 days ) .
Additionally , we included archival MAGIC observations and data published by the VERITAS collaboration in these studies .
For the correlation studies , LS I +61 ^ { \circ } 303 has also been observed during the orbital phases where sporadic VHE emission had been detected in the past ( \phi = 0.75 – 1.0 ) .
These MAGIC observations were simultaneous with optical spectroscopy from the LIVERPOOL telescope .

Results : The TeV flux of the periodical outburst in orbital phases \phi = 0.5 – 0.75 was found to show yearly variability consistent with the long-term modulation of \sim 4.5 years found in the radio band .
This modulation of the TeV flux can be well described by a sine function with a best-fit period of 1610 \pm 58 days .
The complete data , including archival observations , span two super-orbital periods .
There is no evidence for a correlation between the TeV emission and the mass-loss rate of the Be star , but this may be affected by the strong , short-timescale ( as short as intra-day ) variation displayed by the H \alpha fluxes .

Conclusions :