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

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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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    References listed on IDEAS

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    5. Nielsen, Morten Ørregaard, 2009. "A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1515-1544, December.
    6. Aue, Alexander & Van Delft, Anne, 2017. "Testing for stationarity of functional time series in the frequency domain," LIDAM Discussion Papers ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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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. Morten {O}rregaard Nielsen & Won-Ki Seo & Dakyung Seong, 2023. "Inference on common trends in functional time series," Papers 2312.00590, arXiv.org, revised May 2024.

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    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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