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Functional regression of continuous state distributions

Author

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  • Park, Joon Y.
  • Qian, Junhui

Abstract

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

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    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. Benatia, David & Carrasco, Marine & Florens, Jean-Pierre, 2017. "Functional linear regression with functional response," Journal of Econometrics, Elsevier, vol. 201(2), pages 269-291.
    3. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.
    4. Gadea Rivas, María Dolores & Gonzalo, Jesús, 2020. "Trends in distributional characteristics: Existence of global warming," Journal of Econometrics, Elsevier, vol. 214(1), pages 153-174.
    5. Yoosoon Chang & Ana María Herrera & Elena Pesavento, 2023. "Oil prices uncertainty, endogenous regime switching, and inflation anchoring," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 820-839, September.
    6. Yoosoon Chang & Fabio Gómez-Rodríguez & Mr. Gee Hee Hong, 2022. "The Effects of Economic Shocks on Heterogeneous Inflation Expectations," IMF Working Papers 2022/132, International Monetary Fund.
    7. Imaizumi, Masaaki & Kato, Kengo, 2018. "PCA-based estimation for functional linear regression with functional responses," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 15-36.
    8. Salish, Nazarii & Gleim, Alexander, 2019. "A moment-based notion of time dependence for functional time series," Journal of Econometrics, Elsevier, vol. 212(2), pages 377-392.
    9. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    10. Meeks, Roland & Monti, Francesca, 2023. "Heterogeneous beliefs and the Phillips curve," Journal of Monetary Economics, Elsevier, vol. 139(C), pages 41-54.
    11. Yoosoon Chang & Steven N. Durlauf & Seunghee Lee & Joon Y. Park, 2023. "A Trajectories-Based Approach to Measuring Intergenerational Mobility," NBER Working Papers 31020, National Bureau of Economic Research, Inc.
    12. Won‐Ki Seo, 2024. "Functional principal component analysis for cointegrated functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 320-330, March.
    13. Yoosoon Chang & J. Isaac Miller & Joon K. Park, 2024. "Shocking Climate: Identifying Economic Damages from Anthropogenic and Natural Climate Change," CAEPR Working Papers 2024-007 Classification-E, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    14. Hilde C. Bjørnland & Yoosoon Chang & Jamie L. Cross, 2023. "Oil and the Stock Market Revisited: A Mixed Functional VAR Approach," CAMA Working Papers 2023-18, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    15. 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).
    16. Chang, Yoosoon & Kaufmann, Robert K. & Kim, Chang Sik & Miller, J. Isaac & Park, Joon Y. & Park, Sungkeun, 2020. "Evaluating trends in time series of distributions: A spatial fingerprint of human effects on climate," Journal of Econometrics, Elsevier, vol. 214(1), pages 274-294.
    17. Yoosoon Chang & Soyoung Kim & Joon Y. Park, 2025. "How Do Macroaggregates and Income Distribution Interact Dynamically? A Novel Structural Mixed Autoregression with Aggregate and Functional Variables," Working Papers No 01/2025, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    18. 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.
    19. 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.
    20. Seo, Won-Ki & Beare, Brendan K., 2019. "Cointegrated linear processes in Bayes Hilbert space," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 90-95.
    21. 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.
    22. 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.

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    More about this item

    Keywords

    Functional regression; Time-varying density; Moment dependence;
    All these keywords.

    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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