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Limit theory and inference in non-cointegrated functional coefficient regression

Author

Listed:
  • Wang, Ying
  • Phillips, Peter C.B.
  • Tu, Yundong

Abstract

Functional coefficient (FC) cointegrating regressions offer empirical investigators flexibility in modeling economic relationships by introducing covariates that influence the direction and intensity of comovement among nonstationary time series. FC regression models are also useful when formal cointegration is absent, in the sense that the equation errors may themselves be nonstationary, but where the nonstationary series display well-defined FC linkages that can be meaningfully interpreted as correlation measures involving the covariates. The present paper proposes new nonparametric estimators for such FC regression models where the nonstationary series display linkages that enable consistent estimation of the correlation measures between them. Specifically, we develop n-consistent estimators for the functional coefficient and establish their asymptotic distributions, which involve mixed normal limits that facilitate inference. Two novel features that appear in the limit theory are (i) the need for non-diagonal matrix normalization due to the presence of stationary and nonstationary components in the regression; and (ii) random bias elements that appear in the asymptotic distribution of the kernel estimators, again resulting from the nonstationary regression components. Numerical studies reveal that the proposed estimators achieve significant efficiency improvements compared to the estimators suggested in earlier work by Sun et al. (2011). Easily implementable specification tests with standard chi-square asymptotics are suggested to check for constancy of the functional coefficient. These tests are shown to have faster divergence rate under local alternatives and enjoy superior performance in simulations than tests proposed in Gan et al. (2014). An empirical application based on the quantity theory of money is included, illustrating the practical use of correlated but non-cointegrated regression relations.

Suggested Citation

  • Wang, Ying & Phillips, Peter C.B. & Tu, Yundong, 2025. "Limit theory and inference in non-cointegrated functional coefficient regression," Journal of Econometrics, Elsevier, vol. 249(PB).
  • Handle: RePEc:eee:econom:v:249:y:2025:i:pb:s0304407625000508
    DOI: 10.1016/j.jeconom.2025.105996
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    More about this item

    Keywords

    Cointegration; Correlation measure; Functional coefficient regression; Marginal integration; Nonstationary time series;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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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