Correlation theory of almost periodically correlated processes
Journal of Multivariate Analysis
The econometric analysis of seasonal time series
The econometric analysis of seasonal time series
Cyclostationarity: half a century of research
Signal Processing
Bibliography on cyclostationarity
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IEEE Transactions on Signal Processing
Statistical tests for presence of cyclostationarity
IEEE Transactions on Signal Processing
Nonparametric time series analysis for periodically correlated processes
IEEE Transactions on Information Theory
Asymptotic analysis of a fast algorithm for efficient multiple frequency estimation
IEEE Transactions on Information Theory
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The aim of this article is to present a non-parametric way to identify and estimate the unknown frequencies in the Fourier representation of mean function for almost periodically correlated time series. We state the exact form of asymptotic distribution of normalized estimator of Fourier coefficient for fixed frequency in considered class of time series. Next, we prove the consistency of subsampling procedure applied for the Fourier coefficient. Based on these results we propose a graphical method for determining the presence of periodic or almost periodic structure of mean function. Finally, following Walker (1971) [37] we construct a consistent estimator of frequency and corresponding Fourier coefficient.