Jinyuan Chang, Qin Fang, Xinghao Qiao, Qiwei Yao
arXiv 2 Jun 2024 · Statistics — Methodology · publishedJournal of the American Statistical Association (2024) · 10 citations (OpenAlex)
arXiv:2406.00700 · PDF · DOI · OpenAlex · Extracted main text
We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series $p$ is large in relation to the length of time series $n$. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Tang, Shang \ Yang (2022) Clustering and forecasting multiple functional time series, The Annals of Applied Statistics 16: 2523–2553 | 0.928 | 4 | 3 | 100% |
| 2 | Bathia, Yao \ Ziegelmann (2010) Identifying the finite dimensionality of curve time series, The Annals of Statistics 38: 3352–3386 | 0.874 | 5 | 2 | 100% |
| 3 | Chang, Guo \ Yao (2018) Principal component analysis for second-order stationary vector time series, The Annals of Statistics 46: 2094–2124 | 0.811 | 4 | 2 | 100% |
| 4 | Gao, Shang \ Yang (2019) High-dimensional functional time series forecasting: an application to age-specific mortality rates, Journal of Multivariate Ana… | 0.737 | 3 | 2 | 100% |
| 5 | Guo \ Qiao (2023) On consistency and sparsity for high-dimensional functional time series with application to autoregressions, Bernoulli 29: 451–472 | 0.737 | 3 | 2 | 100% |
| 6 | Hörmann, Kidziński \ Hallin (2015) Dynamic functional principal components, Journal of the Royal Statistical Society: Series B. 77: 319–348 | 0.737 | 3 | 2 | 100% |
| 7 | Chiou, Chen \ Yang (2014) Multivariate functional principal component analysis: a normalization approach, Statistica Sinica 24: 1571–1596 | 0.644 | 2 | 2 | 100% |
| 8 | Happ \ Greven (2018) Multivariate functional principal component analysis for data observed on different (dimensional) domains, Journal of the Americ… | 0.644 | 2 | 2 | 100% |
| 9 | Cho, Goude, Brossat \ Yao (2013) Modeling and forecasting daily electricity load curves: a hybrid approach, Journal of the American Statistical Association 108:… | 0.644 | 2 | 2 | 100% |
| 10 | Rice \ Shum (2019) Inference for the lagged cross-covariance operator between functional time series, Journal of Time Series Analysis 40: 665–692 | 0.405 | 1 | 1 | 100% |
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