Linear filtration methods for statistical analysis of periodically correlated random processes—Part I: Coherent and component methods and their generalization

Coherent and component methods for mean and covariance function estimation are analyzed using linear filtration theory. The relationships between variances and biases of the estimates and transfer function of analogue linear filter are determined. On the basis of derived equations the comparison of both techniques are done. The method for obtaining the minimum period-averaged variance estimates is given.

► The coherent and the component methods are partial cases of a linear filtration method. ► Variances and biases of mean and covariance function estimates are firm by properties of shift function of analogue linear filter. ► The variances of the estimates depend on the area under the transfer function absolute values curve. ► The estimator with minimal error is built.