THEORETICAL PREDICTION OF PERIODICALLY CORRELATED
SEQUENCES

Abstract: The paper deals with a spectral analysis and prediction of periodically correlated
(PC) sequences. In particular, a moving average representation of a predictor is obtained and
its coefficients are described in the language of outer factors of spectral line densities of the
sequence. A comprehensive and self-contained overview of the spectral theory of PC
sequences is included. The developed technique is used to compute the spectrum and an
optimal moving average representation of a PC solution to a PARMA system of equations.

1991 AMS Mathematics Subject Classification: 60G25, 62M15, 62M10.

Key words and phrases: Periodically Correlated Sequence, Prediction, PARMA System,
Stationary Sequence.