| 概要 |
The DECOMP (e.g., Kitagawa, 2010) is a seasonal adjustment method that decomposes a given time-series into several components, e.g., trend, seasonal, autoregressive (AR), and observation noise components, in the framework of the state-space modeling. The trend component extracts a trend having much longer wavelength than the time window, the seasonal component extracts a periodic variation having a specific period, and the AR component extracts a variation having several peaks in its power spectrum.
The DECOMP has been broadly applied to various fields, e.g., geomagnetic data (Nagao et al., 2002, 2003), tide gauge data (Nagao et al., 2013), and seismic data in the case of the solid earth science. The components are simultaneously determined in accordance with their system models, in which the backward shift operators are appropriately defined to achieve a unique decomposition. The conventional DECOMP has a room for improvements in the following points: (1) only a single seasonal component is allowed in an observation model, and (2) no method exists, in the case of a multivariate time-series, to update the AR component with satisfying its stationarity based on the gradient of a cost function.
The present study proposes an improvement for DECOMP, generalizing Haba (2019, master’s thesis), that enables us to extract an arbitrary number of seasonal components from a given time-series. A unique decomposition is possible by defining the backward shift operators for the seasonal component based on the set of cyclotomic polynomials. A usage of the AR component can be avoided letting the observation model include a number of seasonal components. A simulation based on synthetic data shows the proposed method performs properly.
We believe that the proposed DECOMP can be another spectrum analysis method in time domain, which does not require pretreatments or interpolations of missing data in the case of Fourier analyses.
References
Kitagawa, G., Introduction to Time Series Modeling, Chapman and Hall, CRC Press, 2010.
Nagao, H., T. Higuchi, T. Iyemori, S. Nakano, and T. Araki, Local time features of geomagnetic jerks, Earth Planets Space, Vol. 54, pp. 117-131, doi:10.1186/BF03351712, 2002.
Nagao, H., T. Iyemori, T. Higuchi, and T. Araki, Lower mantle conductivity anomalies estimated from geomagnetic jerks, Journal of Geophysical Research Solid Earth, Vol. 108, doi:10.1029/2002JB001786, 2003.
Nagao, H., T. Higuchi, S. Miura, and D. Inazu, Time-series modeling of tide gauge records for monitoring of the crustal activities related to oceanic trench earthquakes around Japan The Computer Journal, Vol. 56, No. 3, pp. 355-364, doi:10.1093/comjnl/bxs139, 2013.
Haba, Master’s Thesis, Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 2019 (in Japanese).
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