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3 Makagon A.

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Innovation and factorization of the density of a regular PC sequence

Makagon A.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 1

15--30

In this paper we study an innovation representation of a periodically correlated (PC) sequence and describe the factorization of the densities of a regular PC sequence generated by its innovation. As a byproduct we obtain a certain factorization of vector analytic functions which may be of interest in the theory of Hardy spaces.

Stationary sequences associated with a periodically correlated sequence

Makagon A.

Probability and Mathematical Statistics

2011

Vol. 31, Fasc. 2

263--283

Arranging a periodically correlated sequence (PC) with period T into blocks of length T generates a T-dimensional stationary sequence. In this paper we discuss two other transformations that map PC sequences into T-dimensional stationary sequences and study their properties. We also indicate possible applications of these mappings in the theory of PC processes and, in particular, for study of PARMA systems. The presented construction is both a simplification and enhancement of the construction given in [20].

Theoretical prediction of periodically correlated sequences

Makagon A.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

287--322

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.