Simulation Comparison of CBB and GSBB in Overall Mean Estimation Problem for PC Time Series

  • Anna E. DudekEmail author
  • Paweł Potorski
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


In the chapter the performance comparison in the simulation study of the block bootstrap methods that can be used in the problem of the overall mean estimation of a PC time series is presented. Two block bootstrap techniques are considered: the Circular Block Bootstrap and the circular version of the Generalized Seasonal Block Bootstrap. The actual coverage probabilities of the bootstrap equal-tailed confidence intervals are calculated for a wide range of the block length choices and a few sample sizes. Moreover, the optimal values of the block lengths are pointed. In the most of the considered cases performance of CBB and GSBB is very comparable.


Coverage Probability Block Length Period Length Block Bootstrap Discrete Uniform Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Research of Anna Dudek was partially supported by the Polish Ministry of Science and Higher Education and AGH local grant.


  1. Antoni J (2009) Cyclostationarity by examples. Mech Syst Sign Process 23(4):987–1036CrossRefGoogle Scholar
  2. Bloomfield P, Hurd HL, Lund R (1994) Periodic correlation in stratospheric ozone data. J Time Ser Anal 15:127–150CrossRefzbMATHMathSciNetGoogle Scholar
  3. Bloomfield P, Hurd HL, Lund RB, Smith R (1995) Climatological time series with periodic correlation. J Clim 8:2787–2809CrossRefGoogle Scholar
  4. Chan V, Lahiri SN, Meeker WQ (2004) Block bootstrap estimation of the distribution of cumulative outdoor degradation. Technometrics 46:215–224CrossRefMathSciNetGoogle Scholar
  5. Dudek AE, Hurd H, Wójtowicz W (2013) perARMA: package for periodic time series analysis, R package version 1.5.
  6. Dudek AE, Leśkow J, Politis D, Paparoditis E (2014) A generalized block bootstrap for seasonal time series. J Time Ser Anal. doi: 10.1002/jtsa.12053. Accessed 27 NOV 2013
  7. Hurd HL, Miamee AG (2007) Periodically correlated random sequences: spectral theory and practice. Wiley, HobokenCrossRefGoogle Scholar
  8. Jones R, Brelsford W (1967) Time series with periodic structure. Biometrika 54:403–408zbMATHMathSciNetGoogle Scholar
  9. Leśkow J, Synowiecki R (2010) On bootstrapping periodic random arrays with increasing period. Metrika 71:253–279CrossRefzbMATHMathSciNetGoogle Scholar
  10. Politis DN (2001) Resampling time series with seasonal components, in frontiers in data mining and bioinformatics. In: Proceedings of the 33rd symposium on the interface of computing science and statistics, Orange County, CA, 13–17 June 2001, pp 619–621Google Scholar
  11. Politis DN, Romano JP (1992) A circular block-resampling procedure for stationary data. Wiley series in probability and mathematical statistics: probability and mathematical statistics. Wiley, New York, pp 263–270Google Scholar
  12. Synowiecki R (2007) Consistency and application of moving block bootstrap for nonstationary time series with periodic and almost periodic structure. Bernoulli 13(4):1151–1178CrossRefzbMATHMathSciNetGoogle Scholar
  13. Synowiecki R (2008) Metody resamplingowe w dziedzinie czasu dla niestacjonarnych szeregów czasowych o strukturze okresowej i prawie okresowej. PhD Thesis at the Departement of Applied Mathematics, AGH University of Science and Technology, Krakow, Poland.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.AGH University of Science and TechnologyKrakowPoland

Personalised recommendations