IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v104y2016icp209-222.html
   My bibliography  Save this article

Robust methods for heteroskedastic regression

Author

Listed:
  • Atkinson, Anthony C.
  • Riani, Marco
  • Torti, Francesca

Abstract

Heteroskedastic regression data are modelled using a parameterized variance function. This procedure is robustified using a method with high breakdown point and high efficiency, which provides a direct link between observations and the weights used in model fitting. This feature is vital for the application, the analysis of international trade data from the European Union. Heteroskedasticity is strongly present in such data, as are outliers. A further example shows that the new method outperforms ordinary least squares with heteroskedasticity robust standard errors, even when the form of heteroskedasticity is mis-specified. A discussion of computational matters concludes the paper. An appendix presents the new scoring algorithm for estimation of the parameters of heteroskedasticity.

Suggested Citation

  • Atkinson, Anthony C. & Riani, Marco & Torti, Francesca, 2016. "Robust methods for heteroskedastic regression," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 209-222.
    • Handle: RePEc:eee:csdana:v:104:y:2016:i:c:p:209-222
    DOI: 10.1016/j.csda.2016.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316301578
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.07.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    2. Neykov, N.M. & Filzmoser, P. & Neytchev, P.N., 2012. "Robust joint modeling of mean and dispersion through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 34-48, January.
    3. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466, April.
    4. Atkinson, A.C. & Riani, M., 2007. "Exploratory tools for clustering multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 272-285, September.
    5. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Søren Johansen & Bent Nielsen, 2016. "Rejoinder: Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 374-381, June.
    8. Cheng, Tsung-Chi, 2011. "Robust diagnostics for the heteroscedastic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1845-1866, April.
    9. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
    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. Grossi, Luigi & Nan, Fany, 2019. "Robust forecasting of electricity prices: Simulations, models and the impact of renewable sources," Technological Forecasting and Social Change, Elsevier, vol. 141(C), pages 305-318.

    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. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    2. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    3. Andrew B. Martinez, 2020. "Forecast Accuracy Matters for Hurricane Damage," Econometrics, MDPI, vol. 8(2), pages 1-24, May.
    4. Castle, Jennifer L. & Doornik, Jurgen A. & Hendry, David F., 2023. "Robust Discovery of Regression Models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 31-51.
    5. Anthony C. Atkinson & Andrea Cerioli & Marco Riani, 2016. "Discussion of ‘Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models’ by Johansen and Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 349-352, June.
    6. Sullivan Hué, 2022. "GAM(L)A: An econometric model for interpretable machine learning," French Stata Users' Group Meetings 2022 19, Stata Users Group.
    7. Corbellini, Aldo & Magnani, Marco & Morelli, Gianluca, 2021. "Labor market analysis through transformations and robust multivariate models," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    8. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    9. Emmanuel Flachaire & Gilles Hacheme & Sullivan Hu'e & S'ebastien Laurent, 2022. "GAM(L)A: An econometric model for interpretable Machine Learning," Papers 2203.11691, arXiv.org.
    10. James Reade & Genaro Sucarrat, 2016. "General-to-Specific (GETS) Modelling And Indicator Saturation With The R Package Gets," Economics Series Working Papers 794, University of Oxford, Department of Economics.
    11. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "The power of monitoring: how to make the most of a contaminated multivariate sample," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 559-587, December.
    12. Ericsson, Neil R., 2016. "Eliciting GDP forecasts from the FOMC’s minutes around the financial crisis," International Journal of Forecasting, Elsevier, vol. 32(2), pages 571-583.
    13. Anjum, Zeba & Burke, Paul J. & Gerlagh, Reyer & Stern, David I., "undated". "Modeling the Emissions-Income Relationship Using Long-Run Growth Rates," Working Papers 249422, Australian National University, Centre for Climate Economics & Policy.
    14. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    15. Ansgar Belke & Robert Czudaj, 2010. "Is Euro Area Money Demand (Still) Stable? Cointegrated VAR Versus Single Equation Techniques," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot, Berlin, vol. 56(4), pages 285-315.
    16. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    17. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "The analysis of marked and weighted empirical processes of estimated residuals," Economics Papers 2019-W03, Economics Group, Nuffield College, University of Oxford.
    18. Søren Johansen & Lukasz Gatarek, 2014. "Optimal hedging with the cointegrated vector autoregressive model," CREATES Research Papers 2014-40, Department of Economics and Business Economics, Aarhus University.
    19. Dufour, Jean-Marie & Khalaf, Lynda & Bernard, Jean-Thomas & Genest, Ian, 2004. "Simulation-based finite-sample tests for heteroskedasticity and ARCH effects," Journal of Econometrics, Elsevier, vol. 122(2), pages 317-347, October.
    20. Torti, Francesca & Corbellini, Aldo & Atkinson, Anthony C., 2021. "fsdaSAS: a package for robust regression for very large datasets including the batch forward search," LSE Research Online Documents on Economics 109895, London School of Economics and Political Science, LSE Library.

    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:csdana:v:104:y:2016:i:c:p:209-222. 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/locate/csda .

    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.