A central limit theorem for estimation in Gaussian stationary time series observed at unequally spaced times

The central limit theorem is proved for estimates of parameters which specify the covariance structure of a zero mean, stationary, Gaussian, discrete time series observed at unequally spaced times. The estimates considered are obtained by a single iteration from consistent estimates. The result also applies to the maximum likelihood estimate if it is consistent although consistency is not proved here. The essential condition on the sampling times is that the finite sample information matrix, when divided by the sample size, has a limit which is nonsingular and has finite norm. Some examples are presented to illustrate this condition.Gaussian time series martingale differences central limit theorem missing or unequally spaced data