We present results of fitting the 50-day time series of photometry of \alpha Cen A taken by the WIRE satellite in 1999 . Both power spectrum and autocovariance function ( ACF ) fitting techniques were used in an attempt to determine mode frequencies , rotational splittings , lifetimes and amplitudes of low- \ell p-modes . In all , using both techniques , we managed to fit 18 modes ( seven \ell = 0 , eight \ell = 1 and three \ell = 2 ) with frequencies determined to within 1 - 2 \mu Hz . These estimates are shown to be 0.6 \pm 0.3 \mu Hz lower , on average , than the frequencies determined from two other more recent studies ( Bouchy & Carrier 2002 ; Bedding et al . 2004 ) , which used data gathered about 19 months after the WIRE observations . This could be indicative of an activity cycle , although due to the large uncertainty , more data would be needed to confirm this . Over a range of 1700 to 2650 \mu Hz we were also able to use the ACF fitting to determine an average lifetime of 3.9 \pm 1.4 days , and an average rotational splitting of 0.54 \pm 0.22 \mu Hz , which is the first ever reliable estimate of this parameter . In contrast to the ACF , the power spectrum fitting was shown to return significantly biased results for these parameters .