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Simultaneous Inference of a Partially Linear Model in Time Series

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  • Jiaqi Li
  • Likai Chen
  • Kun Ho Kim
  • Tianwei Zhou

Abstract

We introduce a new methodology to conduct simultaneous inference of the nonparametric component in partially linear time series regression models where the nonparametric part is a multivariate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the multivariate function by extending the high-dimensional Gaussian approximation to dependent processes with continuous index sets. Our results allow for a more general dependence structure compared to previous works and are widely applicable to a variety of linear and nonlinear autoregressive processes. We demonstrate the validity of our proposed methodology by examining the finite-sample performance in the simulation study. Finally, an application in time series, the forward premium regression, is presented, where we construct the SCR for the foreign exchange risk premium from the exchange rate and macroeconomic data.

Suggested Citation

  • Jiaqi Li & Likai Chen & Kun Ho Kim & Tianwei Zhou, 2022. "Simultaneous Inference of a Partially Linear Model in Time Series," Papers 2212.10359, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2212.10359
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    References listed on IDEAS

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    1. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
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    3. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    4. Liang, Hua & Härdle, Wolfgang & Werwatz, Axel, 1997. "Asymptotic properties of the nonparametric part in partial linear heteroscedastic regression models," SFB 373 Discussion Papers 1997,55, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
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