Skip to main content
SpringerLink
Log in
Book cover

The International Conference on Cyber Security Intelligence and Analytics

CSIA 2021: Cyber Security Intelligence and Analytics pp 369–376Cite as

Ratio Test for Time-Varying Variance of Mean Change Point Based on Big Data Analysis

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1342))

Abstract

There are more and more applications involve the big data analytics. The research method of big data is particularly important in the study of time-varying volatilities. In the article, we analysis the tests for a constant mean possibly subjected to change under strong mixing dependence based on big data method. The change point methods provided here rely on ratio type test statistics based on the functional of the partial sums of residuals. The main advantage of proposed approach is that the model allows strong mixing and time-varying variance in error terms. Based on the fundamental results suggested by Cavaliere (2004, Econometric Reviews, 23, 259− 292), the limiting distribution under the original hypothesis is derived and the consistency under the alternatives is also proved.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Page, M.E.: Continuous inspection schemes. Biometrika 42, 100–114 (1954)

    Article  MathSciNet  Google Scholar 

  2. Perron, P.: Dealing with structural breaks. Palgrave Handb. Econometrics 1, 278–352 (2006)

    Google Scholar 

  3. Chen, J., Gupta, A.K.: Parametric Statistical Change Point Analysis: With Applications to Genetics, and Finance. Springer Science and Business Media, Berlin (2011)

    Google Scholar 

  4. Brodsky, E., Darkhovsky, B.S.: Nonparametric Methods in the Problems of Change Points. Springer Science & Business Media, Berlin (2013)

    MATH  Google Scholar 

  5. Bai, J.: Least squares estimation of a shift in linear processes. J. Time Ser. Anal. 15, 453–472 (1994)

    Article  MathSciNet  Google Scholar 

  6. Shao, X.F.: A simple test of changes in mean in the possible presence of long-range dependence. J. Time Ser. Anal. 32, 598–606 (2010)

    Article  MathSciNet  Google Scholar 

  7. Aue, A., Horváth, L.: Structural breaks in time series. J. Time Ser. Anal. 34, 1–16 (2013)

    Article  MathSciNet  Google Scholar 

  8. Zhao, W.Z., Xia, Z.M., Tian, Z.: Ratio test for variance change point in linear process with long memory. Stat. Pap. 51, 397–407 (2010)

    Article  MathSciNet  Google Scholar 

  9. Horváth, L., Horváth, Z., Husková, M.: Ratio tests for change point detection. Inst. Math. Stat. 1, 293–304 (2008)

    MathSciNet  Google Scholar 

  10. Jandhyala, V., Fotopoulos, S., MacNeill, I., Liu, P.: Inference for single and multiple change-points in time series. J. Time Ser. Anal. 34, 423–446 (2013)

    Article  MathSciNet  Google Scholar 

  11. Pagan, A.R., Schwert, G.W.: Testing for covariance stationarity in stock market data. Econ. Lett. 33, 165–170 (1990)

    Article  Google Scholar 

  12. Waston, M.W.: Explaining the increased variability in long-term intest rates. Fed. Reserve Bank Richmond Econ. Quart. 85, 71–96 (1999)

    Google Scholar 

  13. van Dijk, D., Osborn, D.R., Sensier, M.: Change in variability of the business cycle in the G7 countries. Econometric Institute Report (2002)

    Google Scholar 

  14. Kim, T.H., Leybourne, S., Newbold, P.: Unit root tests with a break in innovation variance. J. Econometrics 109, 365–387 (2002)

    Article  MathSciNet  Google Scholar 

  15. Cavaliere, G.: Unit root tests under time-varying variances. Econometric Rev. 23, 259–292 (2004)

    Article  MathSciNet  Google Scholar 

  16. Cavaliere, G., Taylor, A.M.R.: Testing for unit roots in time series models with non-stationary volatility. J. Econometrics 140, 919–947 (2007)

    Article  MathSciNet  Google Scholar 

  17. Zhang, E., Wu, J.: Testing for structural changes in linear regressions with time-varying variance. Communications in Statistics - Theory and Methods, pp. 1–30 (2019)

    Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation of China under Grant No. 71473194; Science and Technology Foundation of Shaanxi Province of China under Grant No. 2020JM513.

Author information

Authors and Affiliations

  1. Department of Sciences, Xi’an University of Science and Technology, Xi’an, 710054, Shannxi, People’s Republic of China

    Caicai Li, Hao Jin & Huihui Bai

Authors
  1. Caicai Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huihui Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Caicai Li .

Editor information

Editors and Affiliations

  1. Shanghai University of Medicine and Health Sciences, Shanghai, China

    Zheng Xu

  2. Department Software Engineering and Game Development, Kennesaw State University, Marietta, GA, USA

    Reza M. Parizi

  3. School of Engineering and Sciences, Tecnologico de Monterrey, Puebla, Mexico

    Octavio Loyola-González

  4. Assistant Professor in Practice, University of Texas at San Antonio, Boerne, TX, USA

    Xiaolu Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Li, C., Jin, H., Bai, H. (2021). Ratio Test for Time-Varying Variance of Mean Change Point Based on Big Data Analysis. In: Xu, Z., Parizi, R.M., Loyola-González, O., Zhang, X. (eds) Cyber Security Intelligence and Analytics. CSIA 2021. Advances in Intelligent Systems and Computing, vol 1342. Springer, Cham. https://doi.org/10.1007/978-3-030-70042-3_53

Download citation

Publish with us

Policies and ethics

Search

Navigation