In this work, the application of the superresolution autoregressive (AR) model to enhance the resolution of the microelectromechanical systems (MEMS) Fourier transform infrared spectrometer (FTIR) spectrometer is studied theoretically and experimentally. The effect of the number of spectral lines, the spacing between the lines, the resolution of the MEMS FTIR spectrometer and the signal-to-noise ratio (SNR) on the prediction accuracy is addressed for different targeted prediction resolutions. The effect of the SNR on applying the AR model is studied. Then, the AR model is applied to experimental data obtained using the MEMS FTIR for the different cases of single spectral line, xenon lamp lines and gas cells containing different gas mixtures. It is found that enhancement up to 4× can obtained in the case of the single line, while an enhancement of about 2-2.5× can be obtained in the case of multilines without having false spectral lines.