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A new method to detect periodically correlated structure

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Abstract

In this paper, we introduce a new method to test whether a discrete-time periodically correlated model explains an observed time series. The proposed method is based on the estimation of the support of spectral measure. Comparisons between our procedure and the methods which were proposed by Broszkiewicz-Suwaj et al. (Phys A 336:196–205, 2004) show that our testing procedure is more powerful. We investigate the performance of the proposed method by using real and simulated datasets.

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References

  • Anderson PL, Meerschaert MM (2005) Parameter estimation for periodically stationary time series. J Time Ser Anal 26:489–518

    Article  MATH  MathSciNet  Google Scholar 

  • Anderson PL, Meerschaert MM, Vecchia A (1999) Innovations algorithm for periodically stationary time series. Stoch Process Appl 83:149–169

    Article  MATH  MathSciNet  Google Scholar 

  • Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57(1):125–133

    MATH  MathSciNet  Google Scholar 

  • Billingsley P (1995) Probability and measure, 3rd edn. Wiley, Hoboken

    MATH  Google Scholar 

  • Bloomfield P, Hurd HL, Lund R (1994) Periodic correlation in stratospheric ozone time series. J Time Ser Anal 15(2):127–150

    Article  MATH  MathSciNet  Google Scholar 

  • Broszkiewicz-Suwaj E (2003) Methods for determining the presence of periodic correlation based on the bootstrap methodology. Hugo Steinhaus Center research report HSC/03/2. http://www.im.pwr.wroc.pl/~hugo/Publications.html

  • Broszkiewicz-Suwaj E, Makagon A, Weron R, Wylomanska A (2004) On detecting and modeling periodic correlation in financial data. Phys A 336:196–205

    Article  MathSciNet  Google Scholar 

  • Franses PH (1996) Periodicity and stochastic trends in economic time series. Oxford University Press, New York

    MATH  Google Scholar 

  • Gardner WA, Franks LE (1975) Characterization of cyclostationary random signal processes. IEEE Trans Inf Theory IT–21:4–14

    Article  MATH  Google Scholar 

  • Gardner WA, Napolitano A, Paura L (2006) Cyclostationarity: half a century of research. Sig Process 86:639–697

    Article  MATH  Google Scholar 

  • Gladyshev EG (1961) Periodically correlated random sequences. Sov Math 2:385–388

    MATH  Google Scholar 

  • Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6(2):65–70

    MATH  MathSciNet  Google Scholar 

  • Hurd HL, Gerr N (1991) Graphical methods for determining the presence of periodic correlation in time series. J Time Ser Anal 12:337–350

    Article  MathSciNet  Google Scholar 

  • Hurd HL, Miamee AG (2007) Periodically correlated sequences: spectral theory and practice. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Mahmoudi MR, Nematollahi AR, Soltani AR (2015) On the detection and estimation of simple processes. Iran J Sci Technol A(39):239–242

    MathSciNet  Google Scholar 

  • Nematollahi AR, Soltani AR, Mahmoudi MR (2016) Periodically correlated modeling by means of the periodograms asymptotic distributions. Stat Pap 1–12. doi:10.1007/s00362-016-0748-9

  • Nord Pool Annual Report (2002) Nord pool ASA

  • Soltani AR, Azimmohseni M (2007a) Periodograms asymptotic distributions in periodically correlated processes and multivariate stationary processes: an alternative approach. J Stat Plan Inference 137:1236–1242

    Article  MATH  MathSciNet  Google Scholar 

  • Soltani AR, Azimmohseni M (2007b) Simulation of real-valued discrete-time periodically correlated gaussian processes with prescribed spectral density matrices. J Time Ser Anal 28(2):225–240

    Article  MATH  MathSciNet  Google Scholar 

  • Soltani AR, Parvardeh A (2006) Simple random measures and simple processes. Theory Probab Appl 50(3):448–462

    Article  MATH  MathSciNet  Google Scholar 

  • Storey JD (2002) A direct approach to false discovery rates. J R Stat Soc Ser B Stat Methodol 64:479–498

    Article  MATH  MathSciNet  Google Scholar 

  • Storey JD, Tibshirani R (2003) Statistical significance for genomewide studies. Proc Natl Acad Sci USA 100:9440–9445

    Article  MATH  MathSciNet  Google Scholar 

  • Strimmer K (2008) fdrtool: a versatile r package for estimating local and tail area-based false discovery rates. Bioinformatics 24:1461–1462

    Article  Google Scholar 

  • Vinod HD, Lopez-de-Lacalle J (2009) Maximum entropy bootstrap for time series: the meboot R package. J Stat Soft 29(5):1–19

    Article  Google Scholar 

Download references

Acknowledgements

We would like to express our very great appreciation to associate editor and reviewer(s) for their valuable and constructive suggestions during the planning and development of this research work.

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Authors and Affiliations

  1. Department of Statistics, College of Science, Fasa University, Fasa, Iran

    Mohammad Reza Mahmoudi

  2. Department of Statistics, Shiraz University, Shiraz, 71454, Iran

    Mohsen Maleki

Authors
  1. Mohammad Reza Mahmoudi
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  2. Mohsen Maleki
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Correspondence to Mohammad Reza Mahmoudi.

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Mahmoudi, M.R., Maleki, M. A new method to detect periodically correlated structure. Comput Stat 32, 1569–1581 (2017). https://doi.org/10.1007/s00180-016-0705-z

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  • DOI: https://doi.org/10.1007/s00180-016-0705-z

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