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Estimation for time-varying coefficient smoothed quantile regression.

Lixia Hu1, Jinhong You2, Qian Huang3

  • 1School of Statistics and Mathematics, Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China.

Journal of Applied Statistics
|July 4, 2025
PubMed
Summary
This summary is machine-generated.

We introduce a new time-varying coefficient regression method called conquer (convolution-type smoothed quantile regression). This method effectively models nonstationary processes and demonstrates strong performance in financial volatility analysis.

Keywords:
Bahadur–Kiefer representationconvolutionlocally stationary processquantile regressiontime-varying coefficient model

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Nonstationary stochastic processes require advanced modeling techniques.
  • Time-varying coefficient regression is crucial for capturing dynamic relationships.
  • Existing methods may not fully address the complexities of locally stationary processes.

Purpose of the Study:

  • To propose and analyze a novel time-varying coefficient regression method, conquer.
  • To develop a local linear estimator for the varying-coefficient function within the conquer framework.
  • To establish the theoretical properties and practical utility of the conquer estimator.

Main Methods:

  • Development of a local linear conquer estimator for time-varying coefficients.
  • Derivation of the global Bahadur-Kiefer representation for asymptotic normality.
  • Investigation of statistical inference, including simultaneous confidence bands.
  • Empirical validation through extensive simulation studies and real-world financial data.

Main Results:

  • The proposed conquer estimator achieves asymptotic normality.
  • The method provides a robust framework for statistical inference, including confidence bands.
  • Simulation studies confirm the finite-sample performance and validity of the asymptotic theory.
  • Successful application to financial volatility data demonstrates practical relevance.

Conclusions:

  • The conquer method offers a powerful tool for analyzing nonstationary time series data.
  • The theoretical results provide a solid foundation for statistical inference in time-varying coefficient models.
  • The approach is well-suited for applications in econometrics and financial modeling.