STOCHASTIC MODELS OF HIDDEN PERIODICITIES AND EFFECTIVE METHODS FOR THEIR DISCOVERY
Presented by Academician of the National Academy of Sciences of Ukraine Z.T. Nazarchuk
DOI:
https://doi.org/10.15407/dopovidi2023.06.019Keywords:
hidden periodicities, periodically non-stationary random processes, quasi-optimal estimators of basic frequencies, convergences in the mean squareAbstract
The methods for discovering hidden periodicities described by periodically non-stationary random processes (PNRP) and the ways to improve their efficiency are considered. The analysis of quasi-optimal estimators for basic frequencies of the first and second-order PNRP moment functions is carried out. These estimators are found as maximum points of the quadratic functional that serves as an asymptotic approximation of the least square functional. Convergences in the mean square of the estimators using the small parameter method are proven, and dependencies of their biases and variances on the realization length and Fourier coefficients of the mean and covariance functions are obtained at the first approximation.
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