We investigate retrieval of the stellar rotation signal for Proxima Centauri .
We make use of high-resolution spectra taken with uves and harps of Proxima Centauri over a 13-year period as well as photometric observations of Proxima Centauri from asas and hst .
We measure the H \alpha equivalent width and H \alpha index , skewness and kurtosis and introduce a method that investigates the symmetry of the line , the Peak Ratio , which appears to return better results than the other measurements .
Our investigations return a most significant period of 82.6 \pm 0.1 days , confirming earlier photometric results and ruling out a more recent result of 116.6 days which we conclude to be an alias induced by the specific harps observation times .
We conclude that whilst spectroscopic H \alpha measurements can be used for period recovery , in the case of Proxima Centauri the available photometric measurements are more reliable .
We make 2D models of Proxima Centauri to generate simulated H \alpha , finding that reasonable distributions of plage and chromospheric features are able to reproduce the equivalent width variations in observed data and recover the rotation period , including after the addition of simulated noise and flares .
However the 2D models used fail to generate the observed variety of line shapes measured by the peak ratio .
We conclude that only 3D models which incorporate vertical motions in the chromosphere can achieve this .