Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A Bayesian time series model with multiple structural change-points for electricity data

  • Kim, Jaehee (Department of Statistics, Duksung Women's University)
  • Received : 2017.05.31
  • Accepted : 2017.07.18
  • Published : 2017.07.31
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Abstract

In this research multiple change-points estimation for South Korean electricity generation data is considered. We analyze the South Korean electricity data via deterministically trending dynamic time series model with multiple structural changes in trends in a Bayesian approach. The number of change-points and the timing are unknown. The goal is to find the best model with the appropriate number of change-points and the length of the segments. A genetic algorithm is implemented to solve this optimization problem with a variable dimension of parameters. We estimate the structural change-points for South Korean electricity generation data and Nile River flow data additionally.

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References

  1. Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica, 61, 821-856. https://doi.org/10.2307/2951764
  2. Andrews, D. W. K., Lee, I. and Ploberger, W. (1996). Optimal changepoint tests for normal linear regression. Journal of Econometrics, 70, 9-38. https://doi.org/10.1016/0304-4076(94)01682-8
  3. Andrews, D. W. K. and Ploberger, W. (1994). Optimal tests when a nuisance parameter is present only under the alternative. Econometrica, 62, 1383-1414. https://doi.org/10.2307/2951753
  4. Bai, J. (1994). Least squares estimation of a shift in linear processes. Journal of Time Series Analysis, 15, 453-472. https://doi.org/10.1111/j.1467-9892.1994.tb00204.x
  5. Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66, 47-78. https://doi.org/10.2307/2998540
  6. Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18, 1-22. https://doi.org/10.1002/jae.659
  7. Bentzen, J. and Engsted, T. (1993). Expectations, adjustment costs, and energy demand. Resources and Energy Economics, 15, 371-385.
  8. Brown, R. L., Durbin, J. and Evans, J. M. (1975). Techniques for testing the constancy of regression relationships over time. Journal of Royal Statistical Society B, 37, 149-192.
  9. Chambers, L. (1995). Practical handbook of genetic algorithms: applications, CRC-Press, Boca Raton, Florida.
  10. Cheon, S. and Kim, J. (2010) Multiple change-point detection of multivariate mean vectors with Bayesian approach. Computational Statistics & Data Analysis, 54, 406-425. https://doi.org/10.1016/j.csda.2009.09.003
  11. Christodoulakis, N. M., Kalyvitis, S. C., Lalas D. P. and Pesmajoglou, S. (2000). Forecasting energy consumption and energy related C02 emissions in Greece: An evaluation of the consequences of the com- munity support framework II and natural gas penetration. Energy Economics, 22, 395-422. https://doi.org/10.1016/S0140-9883(99)00040-7
  12. Cobb, G. W. (1978). The problem of the Nile: Conditional solution to a changepoint problem. Biometrika, 65, 243-251. https://doi.org/10.1093/biomet/65.2.243
  13. Davis, R. A., Lee, T. and Rodriguez, G. A. (2006). Structural break estimation for nonstationary time series models. Journal of American Statistical Association, 101, 223-239. https://doi.org/10.1198/016214505000000745
  14. Davis, R. A., Lee, T. and Rodriguez, G. A. (2008). Break Detection for a Class of Nonlinear Time Series Models. Journal of Time Series Analysis, 29, 834-867. https://doi.org/10.1111/j.1467-9892.2008.00585.x
  15. Garcia, R. and Perron, P. (1996). An analysis of the real interest rate under regime shifts. The Review of Economics and Statistics, 78, 111-125. https://doi.org/10.2307/2109851
  16. Haupt, R. L. and Haupt, S. E. (1998). Practical Genetic Algorithms, Wiley, New York.
  17. Holland, J. H. (1975). Adaptation in natural and artificial systems. The University of Michigan Press, Michigan.
  18. Jann, A. (2000). Multiple change-point detection with a genetic algorithm. Soft Computing-Springer, 4, 68-75. https://doi.org/10.1007/s005000000049
  19. Jeong, C. and Kim, J. (2013). Bayesian multiple structural change-points estimation in time series models with genetic algorithm. Journal of Korean Statistical Society, 42, 459-468. https://doi.org/10.1016/j.jkss.2013.02.001
  20. Karr, C. L. (1995). Adaptive control of an exothermic chemical reaction system using fuzzy logic and genetic algorithms. Hybrid Intelligent Systems-Springer, 187-202.
  21. Kim, J. and Hart, J. D. (2011). A change-point estimator using local fourier series. Journal of Nonparametric Statistics, 23, 83-98. https://doi.org/10.1080/10485251003721232
  22. Kim, J. and Cheon, S. (2010). A Bayesian regime-switching time-series model. Journal of Time Series Analysis, 31, 365-378. https://doi.org/10.1111/j.1467-9892.2010.00670.x
  23. Kim, J. and Lee, S. (2016) Comparison of parametric and nonparametric hazard change-point estimators. Journal of the Korean Data & Information Science Society, 27, 1253-1262. https://doi.org/10.7465/jkdi.2016.27.5.1253
  24. Kim, J. and Cheon, S. (2011). Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo. Computational Statistics, 25, 215-239.
  25. Kramer, W., Ploberger, W. and Alt, R. (1988). Testing for structural change in dynamic models. Econometrica, 56, 1355-1369. https://doi.org/10.2307/1913102
  26. Lee, C. C. and Lee, J. D. (2010). A panel data analysis of the demand for total energy and electricity in OECD countries. Energy Journal, 31, 1-23.
  27. Lee, S., Shim, S. Y. and Kim, J. (2015). Estimation of hazard function and hazard change-point for the rectal cancer data. Journal of the Korean Data & Information Science Society, 26, 1225-1238. https://doi.org/10.7465/jkdi.2015.26.6.1225
  28. Liu, J., Wu, S. and Zidek, J. V. (1997). On segmented multivariate regression. Statistica Sinica, 7, 497-526.
  29. Lumsdaine, R. L. and Papell, D. H. (1997). Multiple trend breaks and the unit-root hypothesis. Review of Economics and Statistics, 79, 212-218. https://doi.org/10.1162/003465397556791
  30. Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution programs 3rd, rev. and extend edition, Springer.
  31. Muller, H. G. (1992). Change-points in nonparametric regression analysis. The Annals of Statistics, 20, 737-761. https://doi.org/10.1214/aos/1176348654
  32. Papell, D. H. and Prodan, R. (2004). The uncertain unit root in US real GDP: Evidence with restricted and unrestricted structural change. Journal of Money, Credit and Banking, 36, 423-427. https://doi.org/10.1353/mcb.2004.0059
  33. Perron, P. (1991). A test for changes in a polynomial trend function for a dynamic time series, Department of Economics, Princeton University.
  34. Perron, P. and Zhu, X. (2005). Structural breaks with deterministic and stochastic trends. Journal of Econometrics, 129, 65-119. https://doi.org/10.1016/j.jeconom.2004.09.004
  35. Wang, J. and Zivot, E. (2000). A Bayesian time series model of multiple structural changes in level, trend, and variance. Journal of Business and Economic Statistics, 18, 374-386.