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—In this paper, we analyze the periodic cycle of honeybees when they have between 7 and 9 days of age. The circadian clock of the bees present very erratic behavior that it is a challenge to detect cycles. In signal processing, there are several methods to detect periodic patterns. In here, we will use a well-known test, named periodogram, to evaluate rhythmicity and estimate the period. Besides, to determine whether or no rhythmicity exists, we estimate the time when the bees behavior starts to be rhythmic. Also, it can occur that the bees behavior never gets rhythmic. The test of rhythmicity is applied consecutively until find out periodicity, if this exists. Furthermore, we carry out the periodicity test for the time series obtained from the actogram. We find out that for bees which time series is visually periodic, our method detects correctly the starting time. However, for bees which time series does not show a cyclic pattern our method fails due to a very erratic time series and that the consecutive test results also will show this erratic behavior. Finally, we classify the bees according to theirs beginning of a periodic cycle, using functional data analysis.
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Principal component analysis of periodically correlated functional time series
Within the framework of functional data analysis, we develop principal component analysis for periodically correlated time series of functions. We define the components of the above analysis including periodic, operator--valued filters, score processes and the inversion formulas. We show that these objects are defined via convergent series under a simple condition requiring summability of the Hilbert--Schmidt norms of the filter coefficients, and that they possess optimality properties. We explain how the Hilbert space theory reduces to an approximate finite--dimensional setting which is implemented in a custom build \verb|R| package. A data example and a simulation study show that the new methodology is superior to existing tools if the functional time series exhibit periodic characteristics.
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- Award ID(s):
- 1737795
- PAR ID:
- 10059529
- Date Published:
- Journal Name:
- Journal of time series analysis
- ISSN:
- 0143-9782
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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