Autoregressive order selection in missing data problems

Maximum likelihood presents a useful solution for the estimation of the parameters of time series models when data are missing. The highest autoregressive (AR) model order that can be computed without numerical problems is limited and depends on the missing fraction. Order selection will be necessary to obtain a good AR model. The best criterion to select an AR order with an accurate spectral estimate is slightly different from the criterion for contiguous data. The penalty for the selection of additional parameters depends on the missing fraction. The resulting maximum likelihood algorithm can give very accurate spectra, sometimes even if less than 1% of the data remains.