DOI QR코드

DOI QR Code

Computational explosion in the frequency estimation of sinusoidal data

  • Zhang, Kaimeng (Department of Statistics, Chonnam National University) ;
  • Ng, Chi Tim (Department of Statistics, Chonnam National University) ;
  • Na, Myunghwan (Department of Statistics, Chonnam National University)
  • 투고 : 2018.04.20
  • 심사 : 2018.06.08
  • 발행 : 2018.07.31

초록

This paper highlights the computational explosion issues in the autoregressive moving average approach of frequency estimation of sinusoidal data with a large sample size. A new algorithm is proposed to circumvent the computational explosion difficulty in the conditional least-square estimation method. Notice that sinusoidal pattern can be generated by a non-invertible non-stationary autoregressive moving average (ARMA) model. The computational explosion is shown to be closely related to the non-invertibility of the equivalent ARMA model. Simulation studies illustrate the computational explosion phenomenon and show that the proposed algorithm can efficiently overcome computational explosion difficulty. Real data example of sunspot number is provided to illustrate the application of the proposed algorithm to the time series data exhibiting sinusoidal pattern.

키워드

참고문헌

  1. Brockwell PJ and Davis RA (1991). Time Series: Theory and Method, Springer, New York.
  2. Choi S, Chang Y, Kim N, Park S, Song S, and Kang H (2014). Performance enhancement of respiratory tumor motion prediction using adaptive support vector regression: Comparison with adaptive neural network method, International Journal of Imaging Systems and Technology, 24, 8-15. https://doi.org/10.1002/ima.22073
  3. Dmitriev AV, Suvorova AV, and Veselovsky IS (2002). Expected hysteresis of the 23-rd solar cycle in the heliosphere, Advances in Space Research, 29, 475-479. https://doi.org/10.1016/S0273-1177(01)00615-9
  4. Li GD, Guan B, Li WK, and Yu PLH (2012). Hysteretic autoregressive time series models, Biometrika, 99, 1-8. https://doi.org/10.1093/biomet/asr046
  5. Ozaki T (2012). Time Series Modeling of Neuroscience Data, CRC Press.
  6. Platonod AA, Gajo ZK, and Szabatin J (1992). General method for sinusoidal frequencies estimation using ARMA algorithms with nonlinear prediction error transformation, IEEE, 5, 441-444.
  7. Powell MJD (2002). UOBYQA: unconstrained optimization by quadratic approximation, Mathematical Programming, Series B, 92, 555-582. https://doi.org/10.1007/s101070100290
  8. Stroebel AM, Bergner M, Reulbach U, Biermann T, Groemer TW, Klein I, and Kornhuber J (2010). Statistical methods for detecting and comparing periodic data and their application to the nycthemeral rhythm of bodily harm: a population based study, Journal of Circadian Rhythms, 8, 1-10. https://doi.org/10.1186/1740-3391-8-1
  9. Suyal V, Prasad A, and Singh HP (2012). Hysteresis in a solar activity cycle, Solar Physics, 276, 407-414. https://doi.org/10.1007/s11207-011-9889-0
  10. Tong G (1990). A Dynamical System Approach, Oxford University Press, Oxford.
  11. White BM, Low DA, Zhao T, et al. (2011). Investigation of a breathing surrogate prediction algorithm for prospective pulmonary gating, Medical Physics, 38, 1587-1595. https://doi.org/10.1118/1.3556589