Efficient estimation of autocorrelation functions of random data with time series models

Sample covariances, estimated as mean-lagged products of random data, are poor and inaccurate fundaments for the non-parametric spectral estimation with tapered and windowed periodograms. However, the autocovariance can be estimated efficiently with a parametric method as transformation of an estimated time series model, if the model type and model order are known a-priori. A recent development in time-series analysis gives the possibility to automatically select the model type and the model order for data with unknown characteristics. After the computation of hundreds of candidate models of different orders and types, a statistical criterion can select a single time series model. The accuracy of this identification from many candidates is sufficient to approach the performance that can be obtained with parametric estimation if the type and the order of the time series model would be known a priori. Hence, the accuracy (mean square error) of parametric covariance estimates is typically the same or better than what can be achieved by non-parametric mean-lagged-product estimates.