Empirical Spectral Analysis of Periodically Correlated Stochastic Processes. An Alternative Approach

The work is devoted to construction and statistical analysis of a “shifted” periodogram intended to serve as a “half-finished product” when constructing an estimate of the spectral density $f_k(\lambda)$, $k\in\mathbb Z$, of a periodically correlated stochastic process $\{\xi(t),t\in\mathbb R\}$. Each modification of the shifted periodogram proposed in the study possesses the following property: its expectation depends on the spectral density $f_k(\lambda)$ only and does not depend on the spectral densities $f_j(\lambda)$, $j\neq k$. The correlation properties of one of the simplest modifications of the shifted periodogram are studied. Two techniques for using the shifted periodogram to construct an estimate of the spectral density $f_k(\lambda)$ are presented.