Estimation of autoregressive spectra with randomly missing data

A Gaussian likelihood is completely determined by the data covariance matrix, which can be characterized for stationary random processes by the parameters of an autoregressive (AR) model. The best AR predictor includes all previous observations if data are incomplete, in contrast with consecutive data where p previous observations determine the best AR(p) prediction. The missing data likelihood will be approximated with only those observations that fall within a finite time interval. The resulting nonlinear estimation algorithm requires no user provided initial solution, is suited for order selection and can give very accurate spectra even if less than 10% of the data remains.