IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v66y2004i2p105-115.html
   My bibliography  Save this article

On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models

Author

Listed:
  • Bischoff, Wolfgang
  • Hashorva, Enkelejd
  • Hüsler, Jürg
  • Miller, Frank

Abstract

Given a Brownian bridge B0 with trend g:[0,1]-->[0,[infinity]), Y(z)=g(z)+B0(z),z[set membership, variant][0,1],we are interested in testing H0:g[reverse not equivalent]0 against the alternative K:g>0. For this test problem we study weighted Kolmogorov testswhere c>0 is a suitable constant and w:[0,1]-->[0,[infinity]) is a weight function. To do such an investigation a recent result of the authors on a boundary crossing probability of the Brownian bridge is useful. In case the trend is large enough we show an optimality property for weighted Kolmogorov tests. Furthermore, an additional property for weighted Kolmogorov tests is shown which is useful to find the more favourable weight for specific test problems. Finally, we transfer our results to the change-point problem whether a regression function is or is not constant during a certain period.

Suggested Citation

  • Bischoff, Wolfgang & Hashorva, Enkelejd & Hüsler, Jürg & Miller, Frank, 2004. "On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 105-115, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:2:p:105-115
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00265-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wolfgang Bischoff & Frank Miller, 2000. "Asymptotically Optimal Tests and Optimal Designs for Testing the Mean in Regression Models with Applications to Change-Point Problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 658-679, December.
    2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    3. Jandhyala, V. K. & MacNeill, I. B., 1989. "Residual partial sum limit process for regression models with applications to detecting parameter changes at unknown times," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 309-323, December.
    4. Hackl, P & Westlund, A H, 1989. "Statistical Analysis of "Structural Change": An Annotated Bibliography," Empirical Economics, Springer, vol. 14(2), pages 167-192.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Enkelejd Hashorva, 2005. "Asymptotics and Bounds for Multivariate Gaussian Tails," Journal of Theoretical Probability, Springer, vol. 18(1), pages 79-97, January.
    2. Deng, Pingjin, 2017. "Boundary non-crossing probabilities for Slepian process," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 28-35.
    3. Bischoff, Wolfgang & Hashorva, Enkelejd, 2005. "A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 265-271, October.
    4. Pingjin Deng, 2016. "Asymptotic of Non-Crossings probability of Additive Wiener Fields," Papers 1610.07131, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    2. Michael W. Robbins & Colin M. Gallagher & Robert B. Lund, 2016. "A General Regression Changepoint Test for Time Series Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 670-683, April.
    3. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    4. Diebold, Francis X. & Chen, Celia, 1996. "Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures," Journal of Econometrics, Elsevier, vol. 70(1), pages 221-241, January.
    5. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    6. Zeileis, Achim & Kleiber, Christian & Kramer, Walter & Hornik, Kurt, 2003. "Testing and dating of structural changes in practice," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 109-123, October.
    7. Aue, Alexander & Horvth, Lajos & Huskov, Marie, 2009. "Extreme value theory for stochastic integrals of Legendre polynomials," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1029-1043, May.
    8. Michael Greenstone & Rema Hanna, 2014. "Environmental Regulations, Air and Water Pollution, and Infant Mortality in India," American Economic Review, American Economic Association, vol. 104(10), pages 3038-3072, October.
    9. Joshy Easaw & Roberto Golinelli, 2022. "Professionals Inflation Forecasts: The Two Dimensions Of Forecaster Inattentiveness [“Sectoral and aggregate inflation dynamics in the euro area”]," Oxford Economic Papers, Oxford University Press, vol. 74(3), pages 701-720.
    10. Evangelos Charalambakis & Yiannis Dendramis & Elias Tzavalis, 2017. "On the determinants of NPLS: lessons from Greece," Working Papers 220, Bank of Greece.
    11. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
    12. Anne Morrison Piehl & Suzanne J. Cooper & Anthony A. Braga & David M. Kennedy, 2003. "Testing for Structural Breaks in the Evaluation of Programs," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 550-558, August.
    13. Zheng, Li & Abbasi, Kashif Raza & Salem, Sultan & Irfan, Muhammad & Alvarado, Rafael & Lv, Kangjuan, 2022. "How technological innovation and institutional quality affect sectoral energy consumption in Pakistan? Fresh policy insights from novel econometric approach," Technological Forecasting and Social Change, Elsevier, vol. 183(C).
    14. Carol Alexander & Anca Dimitriu, 2003. "Equity Indexing: Conitegration and Stock Price Dispersion: A Regime Switiching Approach to market Efficiency," ICMA Centre Discussion Papers in Finance icma-dp2003-02, Henley Business School, University of Reading.
    15. Óscar Bajo Rubio & Carmen Díaz Roldán & Vicente Esteve, 2004. "Is the Fisher Effect Nonlinear? Some Evidence for Spain, 1963-2002," Economic Working Papers at Centro de Estudios Andaluces E2004/05, Centro de Estudios Andaluces.
    16. Jan Gottschalk & Ulrich Fritsche, 2005. "The New Keynesian Model and the Long-Run Vertical Phillips Curve: Does It Hold for Germany?," Discussion Papers of DIW Berlin 521, DIW Berlin, German Institute for Economic Research.
    17. Eksi, Ozan & Tas, Bedri Kamil Onur, 2017. "Unconventional monetary policy and the stock market’s reaction to Federal Reserve policy actions," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 136-147.
    18. Rasmus Fatum & Jesper Pedersen & Peter Norman Sørensen, 2010. "Are the Intraday Effects of Central Bank Intervention on Exchange Rate Spreads Asymmetric and State Dependent?," Discussion Papers 10-20, University of Copenhagen. Department of Economics.
    19. Robin Döttling & Tomislav Ladika & Enrico Perotti, 2016. "The (Self-)Funding of Intangibles," Tinbergen Institute Discussion Papers 16-093/IV, Tinbergen Institute.
    20. Candelon, Bertrand & Lieb, Lenard, 2013. "Fiscal policy in good and bad times," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2679-2694.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:66:y:2004:i:2:p:105-115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.