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INFERENCE ON THE DIMENSION OF THE NONSTATIONARY SUBSPACE IN FUNCTIONAL TIME SERIES

Published online by Cambridge University Press:  28 March 2022

Morten Ørregaard Nielsen Open the ORCID record for Morten Ørregaard Nielsen [Opens in a new window] ,
Won-Ki Seo  and
Dakyung Seong
Morten Ørregaard Nielsen*
Affiliation:
Aarhus University
Won-Ki Seo
Affiliation:
University of Sydney
Dakyung Seong
Affiliation:
University of Sydney
*
Address correspondence to Morten Ørregaard Nielsen, Department of Economics and Business Economics, Aarhus University, Fuglesangs Alle 4, 8210 Aarhus V, Denmark; e-mail: mon@econ.au.dk
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Abstract

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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.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 3 , June 2023 , pp. 443 - 480
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are grateful to the Editor, Co-Editor, two anonymous referees, Brendan Beare, Yoosoon Chang, Joon Park, Peter Phillips, Hanlin Shang, Yundong Tu, and seminar participants at Queen’s University, UC Davis, Australian National University, Boston University, Singapore (SMU/NUS), St. Petersburg State University, the 2019 Canadian Economics Association Conference, the 2019 Time Series and Forecasting Symposium at University of Sydney, the 2020 ANZESG conference, the 2020 Econometric Society World Congress, the 2020 (EC)2 Conference, and the CFE 2020 Conference for comments. An earlier version of this paper was circulated under the title “Variance ratio test for the number of stochastic trends in functional time series.” Nielsen thanks the Canada Research Chairs program and the Social Sciences and Humanities Research Council of Canada for financial support at Queen’s University. Seo thanks the Sir Edward Peacock Postdoctoral Fellowship at Queen’s University for financial support. Data and R code to replicate the empirical results in Table 5 are available on the authors’ websites.

References

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