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

Morten Ørregaard Nielsen, Wonk-ki Seo, Dakyung Seong

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3 Citationer (Scopus)

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.

OriginalsprogEngelsk
TidsskriftEconometric Theory
Vol/bind39
Nummer3
Sider (fra-til)443 - 480
Antal sider38
ISSN0266-4666
DOI
StatusUdgivet - jun. 2023

Emneord

  • cointegration
  • functional data
  • nonstationarity
  • stochastic trends
  • variance ratio

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