We analyze properties of experimental microbial time series and investigate whether stochastic generalized Lotka-Volterra models could reproduce those properties. We show here that (a) to reproduce the relation between the mean absolute differences between successive time points and mean abundance of experimental data, the dominant noise should be linear; (b) to reproduce the distribution of the ratios of abundances between successive time points, the noise should be large; (c) self-interactions should vary over orders of magnitudes to obtain the color of the noise as a function of mean abundances. We stress the fact that all the observed stochastic properties can be obtained from a logistic model with linear noise and without interactions, even the niche character of the experimental time series.