Induced stationary process and structure of locally square integrable periodically correlated processes
Tom 136 / 1999
Studia Mathematica 136 (1999), 71-86 DOI: 10.4064/sm-136-1-71-86
A one-to-one correspondence between locally square integrable periodically correlated (PC) processes and a certain class of infinite-dimensional stationary processes is obtained. The correspondence complements and clarifies Gladyshev's known result  describing the correlation function of a continuous periodically correlated process. In contrast to Gladyshev's paper, the procedure for explicit reconstruction of one process from the other is provided. A representation of a PC process as a unitary deformation of a periodic function is derived and is related to the correspondence mentioned above. Some consequences of this representation are discussed.