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Inference on the dimension of the nonstationary subspace in functional time series

Author

Listed:
  • Morten Ørregaard Nielsen

    (Aarhus University and CREATES)

  • Wonk-ki Seo

    (University of Sydney)

  • Dakyung Seong

    (University of Sydney)

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 US employment rates, Australian temperature curves, and Ontario electricity demand.

Suggested Citation

  • Morten Ørregaard Nielsen & Wonk-ki Seo & Dakyung Seong, 2022. "Inference on the dimension of the nonstationary subspace in functional time series," CREATES Research Papers 2022-04, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2022-04
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/22/rp22_04.pdf
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    References listed on IDEAS

    as
    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. Alexei Onatski & Chen Wang, 2018. "Alternative Asymptotics for Cointegration Tests in Large VARs," Econometrica, Econometric Society, vol. 86(4), pages 1465-1478, July.
    3. Zhang, Rongmao & Robinson, Peter & Yao, Qiwei, 2019. "Identifying cointegration by eigenanalysis," LSE Research Online Documents on Economics 87431, London School of Economics and Political Science, LSE Library.
    4. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    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).
    7. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
    8. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
    9. Ho, Mun S & Sorensen, Bent E, 1996. "Finding Cointegration Rank in High Dimensional Systems Using the Johansen Test: An Illustration Using Data Based Monte Carlo Simulations," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 726-732, November.
    10. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    11. Rongmao Zhang & Peter Robinson & Qiwei Yao, 2019. "Identifying Cointegration by Eigenanalysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 916-927, April.
    12. Chang, Yoosoon & Kim, Chang Sik & Park, Joon Y., 2016. "Nonstationarity in time series of state densities," Journal of Econometrics, Elsevier, vol. 192(1), pages 152-167.
    13. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
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    Cited by:

    1. 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.
    2. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.

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    More about this item

    Keywords

    cointegration; functional data; nonstationarity; stochastic trends; variance ratio;
    All these keywords.

    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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