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Large-Scale Curve Time Series with Common Stochastic Trends

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

arXiv 14 Sep 2025 · Econometrics

arXiv:2509.11060 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies high-dimensional 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-to-implement 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.

Citation extraction

57
references
130
in-text mentions
54
distinct cited
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self-citations
12,754
main-text words

appendix boundary found by appendix_titled_section at “Appendix A:\ Proofs of the main results” · 58% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bai (2004) Estimating cross-section common stochastic trends in nonstationary panel data1.000165100%
2Tavakoli, Nisol and Hallin (2023) Factor models for high-dimensional functional time series II: Estimation and forecasting1.000115100%
3Bai \ Ng (2002) Determining the number of factors in approximate factor models1.00094100%
4Leng et al (2024) Estimating covariance functions for high-dimensional functional time series with dual factor structures1.00064100%
5Barigozzi, Lippi \ Luciani (2021) Large-dimensional dynamic factor models: Estimation of impulse-response functions with I(1) cointegrated factors1.00054100%
6Bai \ Ng (2004) A PANIC attack on unit roots and cointegration1.00054100%
7Tavakoli, Nisol and Hallin (2023) Factor models for high-dimensional functional time series I: Representation results0.87462100%
8Cheng \ Phillips (2009) Semiparametric cointegrating rank selection0.87452100%
9Guo, Qiao and Wang (2021) Factor modelling for high-dimensional functional time series0.87452100%
10Phillips \ Jiang (2025) Cross section curve autoregression: the unit root case0.81142100%

Showing the top 10 of 54 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
11cm Inference on common trends in functional time series0.40511