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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 27, Fasc. 2,
pages 247 - 260
 

SOME RESULTS ON THE SUBSAMPLING FOR $\phi $-MIXING PERIODICALLY STRICTLY STATIONARY TIME SERIES

Rafał Synowiecki

Abstract: The article deals with the special subclass of $\phi $-mixing periodically correlated (PC) time series and the estimation of autocovariance through Fourier coefficients. The aim is to investigate whether the subsampling of the autocovariance estimator is consistent. It is shown that the consistency holds for frequencies $\lambda = 0$ and $\lambda = \pi $. Theoretical reasoning is supplemented with a simulation study.

2000 AMS Mathematics Subject Classification: Primary: 62G09; Secondary: 37M10, 62G20.

Key words and phrases: Periodically correlated time series, subsampling, consistency, $\phi $-mixing property.

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