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Inference On The Dimension Of The Nonstationary Subspace In Functional Time Series

Author

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  • Nielsen, Morten Ørregaard
  • Seo, Won-Ki
  • Seong, Dakyung

Abstract

We propose a statistical procedure to determine the dimension of the nonstationary subspace of cointegrated functional time series taking values in the Hilbert space of square-integrable functions defined on a compact interval. The procedure is based on sequential application of a proposed test for the dimension of the nonstationary subspace. To avoid estimation of the long-run covariance operator, our test is based on a variance ratio-type statistic. We derive the asymptotic null distribution and prove consistency of the test. Monte Carlo simulations show good performance of our test and provide evidence that it outperforms the existing testing procedure. We apply our methodology to three empirical examples: age-specific U.S. employment rates, Australian temperature curves, and Ontario electricity demand.

Suggested Citation

  • Nielsen, Morten Ørregaard & Seo, Won-Ki & Seong, Dakyung, 2023. "Inference On The Dimension Of The Nonstationary Subspace In Functional Time Series," Econometric Theory, Cambridge University Press, vol. 39(3), pages 443-480, June.
    • Handle: RePEc:cup:etheor:v:39:y:2023:i:3:p:443-480_1
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    Cited by:

    1. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.
    2. Kyungsik Nam & Won-Ki Seo, 2025. "Functional Regression with Nonstationarity and Error Contamination: Application to the Economic Impact of Climate Change," Papers 2509.08591, arXiv.org, revised Oct 2025.
    3. 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.
    4. Massimo Franchi & Iliyan Georgiev & Paolo Paruolo, 2024. "Canonical correlation analysis of stochastic trends via functional approximation," Papers 2411.19572, arXiv.org, revised Sep 2025.
    5. Morten {O}rregaard Nielsen & Won-Ki Seo & Dakyung Seong, 2023. "Inference on common trends in functional time series," Papers 2312.00590, arXiv.org, revised Oct 2025.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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