This paper studies high-dimensional integrated curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor model for the latent curves with common trends. A functional PCA technique is applied to estimate the common stochastic trends and functional factor loadings. Under some regularity conditions we derive the mean square convergence and limit distribution theory for the developed estimates, allowing the dimension and sample size to jointly diverge to infinity. We propose an easy-toimplement criterion to consistently select the number of common stochastic trends and further discuss model estimation when the nonstationary factors are cointegrated. Extensive Monte-Carlo simulations and two empirical applications to large-scale temperature curves in Australia and log-price curves of S&P 500 stocks are conducted, showing finite-sample performance and providing practical implementations of the new methodology

Li, Degui; Li, Yu-Ning; Phillips, Peter C.B.

This paper studies high-dimensional integrated curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor model for the latent curves with common trends. A functional PCA technique is applied to estimate the common stochastic trends and functional factor loadings. Under some regularity conditions we derive the mean square convergence and limit distribution theory for the developed estimates, allowing the dimension and sample size to jointly diverge to infinity. We propose an easy-toimplement criterion to consistently select the number of common stochastic trends and further discuss model estimation when the nonstationary factors are cointegrated. Extensive Monte-Carlo simulations and two empirical applications to large-scale temperature curves in Australia and log-price curves of S&P 500 stocks are conducted, showing finite-sample performance and providing practical implementations of the new methodology

Degui Li, Yu-Ning Li and Peter C.B. Phillips
Additional contact information
Degui Li: University of Macau
Yu-Ning Li: University of York
Peter C.B. Phillips: Yale University, University of Auckland

No 202649, Working Papers from University of Macau, Faculty of Business Administration

Keywords: Common trends; Curve time series; Factor models; Functional PCA; High dimensionality (search for similar items in EconPapers)
Pages: 24 pages
Date: 2026-10
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Published in UM-FBA Working Paper Series

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