Niccolò Ajroldi, Jacopo Diquigiovanni, Matteo Fontana, Simone Vantini
arXiv 27 Jul 2022 · Statistics — Methodology · publishedComputational Statistics & Data Analysis (2023) · 13 citations (OpenAlex)
arXiv:2207.13656 · PDF · DOI · OpenAlex · Extracted main text
Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea
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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 | Diquigiovanni, J., Fontana, M., Vantini, S (2022) The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Data self | 1.000 | 8 | 4 | 100% |
| 2 | Diquigiovanni, J., Fontana, M., Vantini, S (2021) Distribution-free prediction bands for multivariate functional time series: an application to the italian gas market self | 1.000 | 6 | 5 | 100% |
| 3 | Chernozhukov, V., Wüthrich, K., Yinchu, Z (2018) Exact and robust conformal inference methods for predictive machine learning with dependent data | 0.961 | 9 | 5 | 89% |
| 4 | Bosq, D (2000) Linear Processes in Function Spaces | 0.928 | 4 | 3 | 100% |
| 5 | Aue, A., Norinho, D., Hörmann, S (2012) On the prediction of stationary functional time series | 0.843 | 4 | 3 | 75% |
| 6 | Horváth, L., Kokoszka, P (2012) Inference for Functional Data with Applications | 0.794 | 6 | 4 | 50% |
| 7 | Lei, J., Rinaldo, A., Wasserman, L (2015) A conformal prediction approach to explore functional data | 0.644 | 2 | 2 | 100% |
| 8 | Papadopoulos, H., Proedrou, K., Vovk, V., Gammerman, A (2002) Inductive confidence machines for regression | 0.644 | 2 | 2 | 100% |
| 9 | Hernández, N., Cugliari, J., Jacques, J (2021) Simultaneous predictive bands for functional time series using minimum entropy sets | 0.644 | 2 | 2 | 100% |
| 10 | Ramsay, J., Silverman, B (2005) Functional Data Analysis | 0.511 | 3 | 2 | 33% |
Showing the top 10 of 39 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Gentle Introduction to Conformal Time Series Forecasting | 0.693 | 6 | 1 |