Estimating time-series models from irregularly spaced data

Maximum-likelihood estimation of the parameters of a continuous-time model for irregularly sampled data is very sensitive to initial conditions. Simulations may converge to a good solution if the true parameters are used as starting values for the nonlinear search of the minimum of the negative log likelihood. From realizable starting values, the convergence to a continuous-time model with an accurate spectrum is rare if more than three parameters have to be estimated. A discrete-time spectral estimator that applies a new algorithm for automatic equidistant missing-data analysis,to irregularly spaced data is introduced. This requires equidistant resampling of the data. A slotted nearest neighbor (NN) resampling method replaces a true irregular observation time instant by the nearest equidistant resampling time point if and only if the distance to the true time is within half the slot width. It will be shown that this new resampling algorithm with the slotting principle has favorable properties over existing schemes such as NN resampling. A further improvement is obtained by using a slot width that is only a fraction of the resampling time.