IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/24135.html
   My bibliography  Save this paper

Bootstrap tests for simple structures in nonparametric time series regression

Author

Listed:
  • Kreiss, Jens-Peter
  • Neumann, Michael H.
  • Yao, Qiwei

Abstract

This paper concerns statistical tests for simple structures such as parametric models, lower order models and additivity in a general nonparametric autoregression setting. We propose to use a modified L2-distance between the nonparametric estimator of regression function and its counterpart under null hypothesis as our test statistic which delimits the contribution from areas where data are sparse. The asymptotic properties of the test statistic are established, which indicates the test statistic is asymptotically equivalent to a quadratic form of innovations. A regression type resampling scheme (i.e. wild bootstrap) is adapted to estimate the distribution of this quadratic form. Further, we have shown that asymptotically this bootstrap distribution is indeed the distribution of the test statistics under null hypothesis. The proposed methodology has been illustrated by both simulation and application to German stock index data.

Suggested Citation

  • Kreiss, Jens-Peter & Neumann, Michael H. & Yao, Qiwei, 2008. "Bootstrap tests for simple structures in nonparametric time series regression," LSE Research Online Documents on Economics 24135, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:24135
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/24135/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lijian Yang & Wolfgang Hardle & Jens Nielsen, 1999. "Nonparametric Autoregression with Multiplicative Volatility and Additive mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 579-604, September.
    2. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    3. Hjellvik, V. & Yao, Q. & Tjostheim, D., 1996. "Linearity Testing using Local Polynomial Approximation," SFB 373 Discussion Papers 1996,60, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Hjellvik, Vidar & Yao, Qiwei & Tjostheim, Dag, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
    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. Fengler, Matthias R. & Mammen, Enno & Vogt, Michael, 2013. "Additive modeling of realized variance: tests for parametric specifications and structural breaks," Economics Working Paper Series 1332, University of St. Gallen, School of Economics and Political Science.
    2. Dabo-Niang, Sophie & Francq, Christian & Zakoian, Jean-Michel, 2009. "Combining parametric and nonparametric approaches for more efficient time series prediction," MPRA Paper 16893, University Library of Munich, Germany.
    3. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    4. Cai, Zongwu & Ren, Yu & Yang, Bingduo, 2015. "A semiparametric conditional capital asset pricing model," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 117-126.
    5. Fengler, M.R. & Mammen, E. & Vogt, M., 2015. "Specification and structural break tests for additive models with applications to realized variance data," Journal of Econometrics, Elsevier, vol. 188(1), pages 196-218.
    6. João Barata R. B. Barroso, 2014. "Behavioral Models of the Foreign Exchange Market: is there any empirical content?," Working Papers Series 364, Central Bank of Brazil, Research Department.
    7. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    8. Enno Mammen & Jens Perch Nielsen & Michael Scholz & Stefan Sperlich, 2019. "Conditional Variance Forecasts for Long-Term Stock Returns," Risks, MDPI, vol. 7(4), pages 1-22, November.
    9. Mammen, Enno & Van Keilegom, Ingrid & Yu, Kyusang, 2013. "Expansion for Moments of Regression Quantiles with Applications to Nonparametric Testing," LIDAM Discussion Papers ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Shimizu, Kenichi, 2014. "Bootstrapping the nonparametric ARCH regression model," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 61-69.

    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. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    2. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    3. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Lag Selection for Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 457-487, July.
    4. Mohamed Chikhi & Claude Diebolt, 2010. "Nonparametric analysis of financial time series by the Kernel methodology," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 865-880, August.
    5. Dette, Holger & Weißbach, Rafael, 2009. "A bootstrap test for the comparison of nonlinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1339-1349, February.
    6. Kim, Woocheol & Linton, Oliver, 2003. "A local instrumental variable estimation method for generalized additive volatility models," LSE Research Online Documents on Economics 2028, London School of Economics and Political Science, LSE Library.
    7. CHIKHI, Mohamed, 2017. "Chocs exogènes et non linéarités dans les séries boursières: Application à la modélisation non paramétrique du cours de l'action Orange [Exogenous Shocks and nonlinearity in the stock exchange seri," MPRA Paper 76691, University Library of Munich, Germany, revised 2017.
    8. Fengler, M.R. & Mammen, E. & Vogt, M., 2015. "Specification and structural break tests for additive models with applications to realized variance data," Journal of Econometrics, Elsevier, vol. 188(1), pages 196-218.
    9. CHIKHI, Mohamed, 2009. "Identification non paramétrique d’un processus non linéaire hétéroscédastique [Nonparametric identification of heteroscedastic nonlinear process]," MPRA Paper 82108, University Library of Munich, Germany, revised 2009.
    10. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
    11. Chikhi, Mohamed & Terraza, Michel, 2002. "Un essai de prévision non paramétrique de l'action France Télécom [A nonparametric prediction test of the France Telecom stock proces]," MPRA Paper 77268, University Library of Munich, Germany, revised Dec 2003.
    12. Heejoon Han & Shen Zhang, 2012. "Non‐stationary non‐parametric volatility model," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 204-225, June.
    13. Ming Chen & Qiongxia Song, 2016. "Semi-parametric estimation and forecasting for exogenous log-GARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 93-112, March.
    14. Yang, Hu & Wu, Xingcui, 2011. "Semiparametric EGARCH model with the case study of China stock market," Economic Modelling, Elsevier, vol. 28(3), pages 761-766.
    15. Vidar Hjellvik & Rong Chen & Dag Tjøstheim, 2004. "Nonparametric Estimation and Testing in Panels of Intercorrelated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 831-872, November.
    16. Lahaye, Jerome & Shaw, Philip, 2014. "Can we reject linearity in an HAR-RV model for the S&P 500? Insights from a nonparametric HAR-RV," Economics Letters, Elsevier, vol. 125(1), pages 43-46.
    17. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness‐of‐fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678, August.
    18. Emeka Nkoro & Aham Kelvin Uko, 2016. "Exchange Rate and Inflation Volatility and Stock Prices Volatility: Evidence from Nigeria, 1986-2012," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 6(6), pages 1-4.
    19. Minot, Nicholas, 2014. "Food price volatility in sub-Saharan Africa: Has it really increased?," Food Policy, Elsevier, vol. 45(C), pages 45-56.
    20. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    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:ehl:lserod:24135. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.