Skip to main content
SpringerLink
Log in

Monitoring Changes in RCA Models

  • Conference paper
  • First Online:
Stochastic Models, Statistics and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 122))

Abstract

In the paper a sequential monitoring scheme is proposed to detect instability of parameters in a random coefficient autoregressive (RCA) time series model of general order p. A given set of historical stable observations is available that serves as a training sample. The proposed monitoring procedure is based on the quasi-likelihood scores and the quasi-maximum likelihood estimators of the respective parameters computed from the training sample, and it is designed so that the sequential test has a small probability of a false alarm and asymptotic power one as the size of the training sample is sufficiently large. The asymptotic distribution of the detector statistic is established under both the null hypothesis of no change as well as under the alternative that a change occurs.

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

Access this chapter

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Anděl J (1976) Autoregressive series with random parameters. Math Operforsch Stat 7:735–741

    Article  MATH  Google Scholar 

  2. Aue A (2004) Strong approximation for RCA(1) time series with applications. Stat Probab Lett 68:369–382

    Article  MathSciNet  MATH  Google Scholar 

  3. Aue A, Horváth L, Steinebach J (2006) Estimation in random coefficient autoregressive models. J Time Ser Anal 27:60–67

    Article  Google Scholar 

  4. Berkes I, Gombay E, Horváth L, Kokoszka P (2004) Sequential change-point detection in GARCH(p,q) models. Econom Theory 20:1140–1167

    Article  MATH  Google Scholar 

  5. Bougerol P, Picard N (1992) Strict stationarity of generalized autoregressive processes. Ann Probab 20:1714–1730

    Article  MathSciNet  MATH  Google Scholar 

  6. Brandt A (1986) The stochastic equation Y n+1=A n Y n +B n with stationary coefficients. Adv Appl Probab 18:211–220

    Article  MATH  Google Scholar 

  7. Chu C-SJ, Stinchcombe M, White H (1996) Monitoring structural change. Econometrica 64:1045–1065

    Article  Google Scholar 

  8. Davidson J (1994) Stochastic limit theory. Advanced texts in econometrics. Oxford University Press, Oxford

    Book  Google Scholar 

  9. Gombay E, Serban D (2009) Monitoring parameter change in AR(p) time series models. J Multivar Anal 100:715–725

    Article  MathSciNet  MATH  Google Scholar 

  10. Horváth L, Hušková M, Kokoszka P, Steinebach J (2004) Monitoring changes in linear models. J Stat Plan Inference 126:225–251

    Article  MATH  Google Scholar 

  11. Horváth L, Rice G (2014) Extensions of some classical methods in change point analysis. Test 23:219–255

    Article  MathSciNet  MATH  Google Scholar 

  12. Hušková M, Koubková A (2006) Sequential procedures for detection of changes in autoregressive sequences. In: Hušková M, Janžura M (eds) Proceedings of Prague stochastics. MATFYZPRESS, Charles University, Prague, pp 437–447

    Google Scholar 

  13. Li F, Tian Z, Qi P (2014) Structural change monitoring for random coefficient autoregressive time series. Commun Stat, Simul Comput. doi:10.1080/03610918.2013.800205

    Google Scholar 

  14. Na O, Lee J, Lee S (2010) Monitoring parameter changes for random coefficient autoregressive models. J Korean Stat Soc 39:281–288

    Article  MathSciNet  MATH  Google Scholar 

  15. Na O, Lee Y, Lee S (2011) Monitoring parameter change in time series models. Stat Methods Appl 20:171–199

    Google Scholar 

  16. Nicholls DF, Quinn BG (1982) Random coefficient autoregressive models: an introduction. Lecture notes in statistics, vol 11. Springer, New York

    Book  MATH  Google Scholar 

  17. Straumann D, Mikosch T (2006) Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: a stochastic recurrence equations approach. Ann Stat 34:2449–2495

    Article  MathSciNet  MATH  Google Scholar 

  18. Truquet L, Yao J (2012) On the quasi-likelihood estimation for random coefficient autoregressions. Statistics 46:505–512

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The work was supported by the Czech Science Foundation project No. P402/12/G097 DYME – Dynamic Models in Economics.

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75, Prague, Czech Republic

    Zuzana Prášková

Authors
  1. Zuzana Prášková
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zuzana Prášková .

Editor information

Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Dept. of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Inst. of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Krzysztof Szajowski

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Prášková, Z. (2015). Monitoring Changes in RCA Models. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_15

Download citation

Publish with us

Policies and ethics

Search

Navigation