IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i14p1473-1478.html
   My bibliography  Save this article

Universal residuals: A multivariate transformation

Author

Listed:
  • Brockwell, A.E.

Abstract

Rosenblatt's transformation has been used extensively for the evaluation of model goodness-of-fit, but it only applies to models whose joint distribution is continuous. In this paper we generalize the transformation so that it applies to arbitrary probability models. The transformation is simple, but has a wide range of possible applications, providing a tool for exploratory data analysis and formal goodness-of-fit testing for a very general class of probability models. The method is demonstrated with specific examples.

Suggested Citation

  • Brockwell, A.E., 2007. "Universal residuals: A multivariate transformation," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1473-1478, August.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:14:p:1473-1478
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00071-5
    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. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    2. N. H. Chan & A. E. Brockwell, 2006. "Long-memory dynamic Tobit models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 351-367.
    3. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    4. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    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. Weiß, Gregor N.F. & Supper, Hendrik, 2013. "Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3334-3350.
    2. Giovanni Angelini & Luca De Angelis, 2017. "PARX model for football match predictions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(7), pages 795-807, November.
    3. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.
    5. Stindl, Tom & Chen, Feng, 2018. "Likelihood based inference for the multivariate renewal Hawkes process," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 131-145.
    6. Tsyplakov, Alexander, 2013. "Evaluation of Probabilistic Forecasts: Proper Scoring Rules and Moments," MPRA Paper 45186, University Library of Munich, Germany.
    7. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    8. Yunwei Cui & Rongning Wu & Qi Zheng, 2021. "Estimation of change‐point for a class of count time series models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1277-1313, December.
    9. Cui, Yunwei & Wu, Rongning, 2016. "On conditional maximum likelihood estimation for INGARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 1-7.
    10. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    11. Claudia Czado & Tilmann Gneiting & Leonhard Held, 2009. "Predictive Model Assessment for Count Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1254-1261, December.
    12. Qijin Cheng & Feng Chen & Paul S F Yip, 2017. "Media effects on suicide methods: A case study on Hong Kong 1998-2005," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-12, April.
    13. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    14. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    15. Tsyplakov, Alexander, 2014. "Theoretical guidelines for a partially informed forecast examiner," MPRA Paper 55017, University Library of Munich, Germany.
    16. Kolassa, Stephan, 2016. "Evaluating predictive count data distributions in retail sales forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 788-803.

    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. Hendry, David F. & Clements, Michael P., 2003. "Economic forecasting: some lessons from recent research," Economic Modelling, Elsevier, vol. 20(2), pages 301-329, March.
    2. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    3. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, September.
    4. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    5. Kapetanios, G. & Mitchell, J. & Price, S. & Fawcett, N., 2015. "Generalised density forecast combinations," Journal of Econometrics, Elsevier, vol. 188(1), pages 150-165.
    6. Deschamps, Philippe J., 2011. "Bayesian estimation of an extended local scale stochastic volatility model," Journal of Econometrics, Elsevier, vol. 162(2), pages 369-382, June.
    7. Ravazzolo Francesco & Rothman Philip, 2016. "Oil-price density forecasts of US GDP," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 441-453, September.
    8. Christian Bontemps & Nour Meddahi, 2012. "Testing distributional assumptions: A GMM aproach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 978-1012, September.
    9. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic Volatility with Leverage: Fast Likelihood Inference," CIRJE F-Series CIRJE-F-297, CIRJE, Faculty of Economics, University of Tokyo.
    10. Rehim Kilic, 2011. "A conditional variance tale from an emerging economy's freely floating exchange rate," Applied Economics, Taylor & Francis Journals, vol. 43(19), pages 2465-2480.
    11. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    12. Coe, Patrick J & Vahey, Shaun P., 2014. "Probablistic Prediction of the US Great Recession with Historical Expert," EMF Research Papers 06, Economic Modelling and Forecasting Group.
    13. Diebold, Francis X. & Schorfheide, Frank & Shin, Minchul, 2017. "Real-time forecast evaluation of DSGE models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 201(2), pages 322-332.
    14. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    15. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    16. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    17. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    18. Leopoldo Catania & Nima Nonejad, 2016. "Density Forecasts and the Leverage Effect: Some Evidence from Observation and Parameter-Driven Volatility Models," Papers 1605.00230, arXiv.org, revised Nov 2016.
    19. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science, revised Aug 2014.
    20. Benedikt Rotermann & Bernd Wilfling, 2015. "Estimating rational stock-market bubbles with sequential Monte Carlo methods," CQE Working Papers 4015, Center for Quantitative Economics (CQE), University of Muenster.

    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:77:y:2007:i:14:p:1473-1478. 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.