Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/taf/jnlbes/v31y2013i4p473-490.html
   My bibliography  Save this article

Constrained Regression for Interval-Valued Data

Author

Listed:
  • Gloria González-Rivera
  • Wei Lin
Abstract
Current regression models for interval-valued data do not guarantee that the predicted lower bound of the interval is always smaller than its upper bound. We propose a constrained regression model that preserves the natural order of the interval in all instances, either for in-sample fitted intervals or for interval forecasts. Within the framework of interval time series, we specify a general dynamic bivariate system for the upper and lower bounds of the intervals. By imposing the order of the interval bounds into the model, the bivariate probability density function of the errors becomes conditionally truncated. In this context, the ordinary least squares (OLS) estimators of the parameters of the system are inconsistent. Estimation by maximum likelihood is possible but it is computationally burdensome due to the nonlinearity of the estimator when there is truncation. We propose a two-step procedure that combines maximum likelihood and least squares estimation and a modified two-step procedure that combines maximum likelihood and minimum-distance estimation. In both instances, the estimators are consistent. However, when multicollinearity arises in the second step of the estimation, the modified two-step procedure is superior at identifying the model regardless of the severity of the truncation. Monte Carlo simulations show good finite sample properties of the proposed estimators. A comparison with the current methods in the literature shows that our proposed methods are superior by delivering smaller losses and better estimators (no bias and low mean squared errors) than those from competing approaches. We illustrate our approach with the daily interval of low/high SP500 returns and find that truncation is very severe during and after the financial crisis of 2008, so OLS estimates should not be trusted and a modified two-step procedure should be implemented. Supplementary materials for this article are available online.

Suggested Citation

  • Gloria González-Rivera & Wei Lin, 2013. "Constrained Regression for Interval-Valued Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 473-490, October.
    • Handle: RePEc:taf:jnlbes:v:31:y:2013:i:4:p:473-490
    DOI: 10.1080/07350015.2013.818004
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07350015.2013.818004
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07350015.2013.818004?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. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    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. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    2. Lin, Wei & González-Rivera, Gloria, 2016. "Interval-valued time series models: Estimation based on order statistics exploring the Agriculture Marketing Service data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 694-711.
    3. Wang, Xun & Zhang, Zhongzhan & Li, Shoumei, 2016. "Set-valued and interval-valued stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 208-223.
    4. Piao Wang & Shahid Hussain Gurmani & Zhifu Tao & Jinpei Liu & Huayou Chen, 2024. "Interval time series forecasting: A systematic literature review," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(2), pages 249-285, March.
    5. Miguel de Carvalho & Gabriel Martos, 2022. "Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 167-180, January.
    6. Gloria Gonzalez-Rivera & Yun Luo & Esther Ruiz, 2018. "Prediction Regions for Interval-valued Time Series," Working Papers 201817, University of California at Riverside, Department of Economics.
    7. Babel Raïssa Guemdjo Kamdem & Jules Sadefo-Kamdem & Carlos Ougouyandjou, 2020. "On Random Extended Intervals and their ARMA Processes," Working Papers hal-03169516, HAL.
    8. Wei Yang & Ai Han & Yongmiao Hong & Shouyang Wang, 2016. "Analysis of crisis impact on crude oil prices: a new approach with interval time series modelling," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1917-1928, December.
    9. Wei Lin & Gloria González‐Rivera, 2019. "Extreme returns and intensity of trading," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1121-1140, November.
    10. Buansing, T.S. Tuang & Golan, Amos & Ullah, Aman, 2020. "An information-theoretic approach for forecasting interval-valued SP500 daily returns," International Journal of Forecasting, Elsevier, vol. 36(3), pages 800-813.
    11. Gloria Gonzalez-Rivera & Wei Lin, 2014. "Interval-valued Time Series: Model Estimation based on Order Statistics," Working Papers 201429, University of California at Riverside, Department of Economics.
    12. Lei, Heng & Xue, Minggao & Liu, Huiling, 2022. "Probability distribution forecasting of carbon allowance prices: A hybrid model considering multiple influencing factors," Energy Economics, Elsevier, vol. 113(C).
    13. Babel Raïssa Guemdjo Kamdem & Jules Sadefo-Kamdem & Carlos Ogouyandjou, 2021. "An Abelian Group way to study Random Extended Intervals and their ARMA Processes," Working Papers hal-03174631, HAL.
    14. Hui Qu & Mengying He, 2022. "Predicting Volatility Based on Interval Regression Models," JRFM, MDPI, vol. 15(12), pages 1-21, November.
    15. Liang-Ching Lin & Hsiang-Lin Chien & Sangyeol Lee, 2021. "Symbolic interval-valued data analysis for time series based on auto-interval-regressive models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 295-315, March.
    16. Sun, Yuying & Han, Ai & Hong, Yongmiao & Wang, Shouyang, 2018. "Threshold autoregressive models for interval-valued time series data," Journal of Econometrics, Elsevier, vol. 206(2), pages 414-446.
    17. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised May 2021.
    18. Sun, Yuying & Zhang, Xun & Hong, Yongmiao & Wang, Shouyang, 2019. "Asymmetric pass-through of oil prices to gasoline prices with interval time series modelling," Energy Economics, Elsevier, vol. 78(C), pages 165-173.
    19. Sun, Yuying & Bao, Qin & Zheng, Jiali & Wang, Shouyang, 2020. "Assessing the price dynamics of onshore and offshore RMB markets: An ITS model approach," China Economic Review, Elsevier, vol. 62(C).
    20. Gloria Gonzalez-Rivera & Yun Luo, 2020. "A Truncated Mixture Transition Model for Interval-valued Time Series," Working Papers 202005, University of California at Riverside, Department of Economics.
    21. Chang, Meng-Shiuh & Ju, Peijie & Liu, Yilei & Hsueh, Shao-Chieh, 2022. "Determining hedges and safe havens for stocks using interval analysis," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    22. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.

    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. Tindara Addabbo & Anna Maccagnan & Carmen Llorca-Rodríguez & Rosa García-Fernández, 2010. "Income distribution and the effect of the financial crisis on the Italian and Spanish labour markets," Department of Economics 0639, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    2. Walter Beckert, 2015. "Choice in the Presence of Experts," Birkbeck Working Papers in Economics and Finance 1503, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    4. Okhrin, Ostap & Ristig, Alexander & Sheen, Jeffrey R. & Trück, Stefan, 2015. "Conditional systemic risk with penalized copula," SFB 649 Discussion Papers 2015-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Xiaohong Chen & Roger Koenker & Zhijie Xiao, 2009. "Copula-based nonlinear quantile autoregression," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 50-67, January.
    6. Magnus, Jan R., 2007. "The Asymptotic Variance Of The Pseudo Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 23(5), pages 1022-1032, October.
    7. Chor-Yiu Sin, 2014. "Qmle Of A Standard Exponential Acd Model: Asymptotic Distribution And Residual Correlation," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 1-10.
    8. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    9. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    10. Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
    11. Manuel Gebetsberger & Jakob W. Messner & Georg J. Mayr & Achim Zeileis, 2017. "Estimation methods for non-homogeneous regression models: Minimum continuous ranked probability score vs. maximum likelihood," Working Papers 2017-23, Faculty of Economics and Statistics, Universität Innsbruck.
    12. David T. Frazier & Bonsoo Koo, 2020. "Indirect Inference for Locally Stationary Models," Monash Econometrics and Business Statistics Working Papers 30/20, Monash University, Department of Econometrics and Business Statistics.
    13. Arie Preminger & Uri Ben-zion & David Wettstein, 2007. "The extended switching regression model: allowing for multiple latent state variables," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(7), pages 457-473.
    14. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    15. Blasques, Francisco & van Brummelen, Janneke & Gorgi, Paolo & Koopman, Siem Jan, 2024. "Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions," Journal of Econometrics, Elsevier, vol. 238(1).
    16. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    17. Hommes, Cars & Zhu, Mei, 2014. "Behavioral learning equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 778-814.
    18. Takagi, Shingo, 1999. "Bias in maximum likelihood estimator of disequilibrium and sample selection model with error-ridden observations," Economics Letters, Elsevier, vol. 64(2), pages 161-165, August.
    19. Hannes Böhm & Julia Schaumburg & Lena Tonzer, 2022. "Financial Linkages and Sectoral Business Cycle Synchronization: Evidence from Europe," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 70(4), pages 698-734, December.
    20. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.

    More about this item

    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:taf:jnlbes:v:31:y:2013:i:4:p:473-490. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UBES20 .

    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.