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Functional regression of continuous state distributions


  • Park, Joon Y.
  • Qian, Junhui


In this paper, we consider a regression model to study the distributional relationship between economic variables. Unlike the classical regression dealing exclusively with mean relationship, our model can be used to analyze the entire dependent structure in distribution. Technically, we treat density functions as random elements and represent the regression relationship as a compact linear operator in the Hilbert spaces of square integrable functions. We propose a consistent estimation procedure for our model, and develop a test to investigate the dependent structure of moments. An empirical example is provided to illustrate how our methodology can be implemented in practical applications.

Suggested Citation

  • Park, Joon Y. & Qian, Junhui, 2012. "Functional regression of continuous state distributions," Journal of Econometrics, Elsevier, vol. 167(2), pages 397-412.
  • Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:397-412
    DOI: 10.1016/j.jeconom.2011.09.024

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    References listed on IDEAS

    1. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Mas, André, 2007. "Weak convergence in the functional autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1231-1261, July.
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    Cited by:

    1. Yoosoon Chang & Robert K. Kaufmann & Chang Sik Kim & J. Isaac Miller & Joon Y. Park & Sungkeun Park, 2015. "Time Series Analysis of Global Temperature Distributions: Identifying and Estimating Persistent Features in Temperature Anomalies," Working Papers 1513, Department of Economics, University of Missouri, revised 25 Jul 2016.
    2. repec:eee:econom:v:201:y:2017:i:2:p:269-291 is not listed on IDEAS
    3. Gonzalo, Jesús & Gadea Rivas, María Dolores, 2017. "Trends in distributional characteristics : Existence of global warming," UC3M Working papers. Economics 24121, Universidad Carlos III de Madrid. Departamento de Economía.
    4. repec:eee:jmvana:v:163:y:2018:i:c:p:15-36 is not listed on IDEAS
    5. ARATA Yoshiyuki, 2017. "A Functional Linear Regression Model in the Space of Probability Density Functions," Discussion papers 17015, Research Institute of Economy, Trade and Industry (RIETI).
    6. Yoosoon Chang & Robert K. Kaufmann & Chang Sik Kim & J. Isaac Miller & Joon Y. Park & Sungkeun Park, 2015. "Evaluating trends in time series of distributions: A spatial fingerprint of human effects on climate," Working Papers 1622, Department of Economics, University of Missouri, revised 19 Dec 2016.
    7. Chang, Yoosoon & Kim, Chang Sik & Park, Joon Y., 2016. "Nonstationarity in time series of state densities," Journal of Econometrics, Elsevier, vol. 192(1), pages 152-167.
    8. Park, Joon Y. & Shin, Kwanho & Whang, Yoon-Jae, 2010. "A semiparametric cointegrating regression: Investigating the effects of age distributions on consumption and saving," Journal of Econometrics, Elsevier, vol. 157(1), pages 165-178, July.
    9. Haugom, Erik & Lien, Gudbrand & Veka, Steinar & Westgaard, Sjur, 2014. "Covariance estimation using high-frequency data: Sensitivities of estimation methods," Economic Modelling, Elsevier, vol. 43(C), pages 416-425.
    10. Soobin Kim & Chang Sik Kim, 2010. "Do S&P 500 and KOSPI Move Together?: A Functional Regression Approach," Korean Economic Review, Korean Economic Association, vol. 26, pages 401-430.

    More about this item


    Functional regression; Time-varying density; Moment dependence;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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