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Cross Section Curve Data Autoregression

Author

Listed:
  • Peter C. B. Phillips

    (Yale University)

  • Liang Jiang

    (Fudan University)

Abstract

This paper develops and applies new asymptotic theory for estimation and inference in parametric autoregression with function valued cross section curve time series. The study provides a new approach to dynamic panel regression with high dimensional dependent cross section data. Here we deal with the stationary case and provide a full set of results extending those of standard Euclidean space autoregression, showing how function space curve cross section data raises efficiency and reduces bias in estimation and shortens confidence intervals in inference. Methods are developed for high-dimensional covariance kernel estimation that are useful for inference. The findings reveal that function space models with wide-domain and narrow-domain cross section dependence provide insights on the effects of various forms of cross section dependence in discrete dynamic panel models with fixed and interactive fixed effects. The methodology is applicable to panels of high dimensional wide datasets that are now available in many longitudinal studies. An empirical illustration is provided that sheds light on household Engel curves among ageing seniors in Singapore using the Singapore life panel longitudinal dataset.

Suggested Citation

  • Peter C. B. Phillips & Liang Jiang, 2025. "Cross Section Curve Data Autoregression," Cowles Foundation Discussion Papers 2439, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2439
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    File URL: https://cowles.yale.edu/sites/default/files/2025-04/d2439.pdf
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    References listed on IDEAS

    as
    1. Kehui Chen & Hans‐Georg Müller, 2012. "Conditional quantile analysis when covariates are functions, with application to growth data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 67-89, January.
    2. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    3. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    4. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    5. Anna Bykhovskaya & Peter C. B. Phillips, 2018. "Boundary Limit Theory for Functional Local to Unity Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(4), pages 523-562, July.
    6. Vinod, H.D. & Shenton, L.R., 1996. "Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value," Econometric Theory, Cambridge University Press, vol. 12(3), pages 481-499, August.
    7. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
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    Full references (including those not matched with items on IDEAS)

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