Younghoon Kim, Marie-Christine Düker, Zachary F. Fisher, Vladas Pipiras
arXiv 19 Jul 2023 · Statistics — Methodology · publishedJournal of Time Series Analysis (2025) · 7 citations (OpenAlex)
arXiv:2307.10454 · PDF · DOI · OpenAlex · Extracted main text
This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters is based on second-order properties of the count and underlying Gaussian time series, yielding estimators of the underlying covariance matrices for which standard principal component analysis applies. Theoretical consistency results are established for the proposed estimation, building on certain concentration results for the models of the type considered. They also involve the memory of the latent Gaussian process, quantified through a spectral gap, shown to be suitably bounded as the model dimension increases, which is of independent interest. In addition, novel cross-validation schemes are suggested for model selection. The forecasting is carried out through a particle-based sequential Monte Carlo, leveraging Kalman filtering techniques. A simulation study and an application are also considered.
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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 | Jia, Y., Kechagias, S., Livsey, J., Lund, R., and Pipiras, V (2023) Latent Gaussian count time series self | 0.950 | 14 | 5 | 86% |
| 2 | Düker, M.-C., Lund, R., and Pipiras, V (2024) High-dimensional latent Gaussian count time series: Concentration results for autocovariances and applications self | 0.950 | 14 | 3 | 86% |
| 3 | Doz, C., Giannone, D., and Reichlin, L (2011) A two-step estimator for large approximate dynamic factor models based on Kalman filtering | 0.807 | 19 | 4 | 53% |
| 4 | Cui, K. and Dunson, D. B (2014) Generalized dynamic factor models for mixed-measurement time series | 0.644 | 2 | 2 | 100% |
| 5 | Harman, H. H. and Jones, W. H (1966) Factor analysis by minimizing residuals (MINRES) | 0.644 | 2 | 2 | 100% |
| 6 | Wang, F. and Wang, H (2018) Modelling non-stationary multivariate time series of counts via common factors | 0.644 | 2 | 2 | 100% |
| 7 | Fan, J., Jiang, B., and Sun, Q (2021) Hoeffding's inequality for general markov chains and its applications to statistical learning | 0.511 | 3 | 2 | 33% |
| 8 | Doucet, A. and Johansen, A. M (2009) A tutorial on particle filtering and smoothing: Fifteen years later | 0.511 | 2 | 1 | 100% |
| 9 | Alzaid, A. A. and Al-Osh, M. A (1993) Some autoregressive moving average processes with generalized Poisson marginal distributions | 0.405 | 1 | 1 | 100% |
| 10 | Andrieu, C. and Doucet, A (2002) Particle filtering for partially observed Gaussian state space models | 0.405 | 1 | 1 | 100% |
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