Estimating Time Series Models from Irregularly Sampled Data

The maximum likelihood estimation of the parameters of the continuous time model for irregularly sampled data is sensitive to initial conditions. Simulations often converge to a good solution if the true parameters are used as the starting values for the nonlinear search of the minimum of the negative log likelihood. From realizable starting values the convergence to a model with an accurate spectrum is rare if more than three parameters have to be estimated. A discrete time spectral estimator is introduced that applies the principles of the algorithm for automatic equidistant missing data analysis to unevenly spaced data. This time series estimator approximates the irregular data by a number of equidistantly resampled missing data sets, with a special nearest neighbor method. Slotted nearest neighbor resampling replaces a true observation time instant by the nearest equidistant resampling time point, if and only if the true time is within half the slot width. A smaller slot will reduce bias. A refined slotted resampling method is introduced, which uses a slot width that is only a fraction of the resampling time, giving multiple data sets with equidistant missing data time sequences which are shifted over the slot width. The highest frequency with accurate spectral estimates can be beyond the mean data rate