Functional Time Series Prediction Under Partial Observation of the Future Curve

References

• Antoniadis, A., Paparoditis, E., and Sapatinas, T. (2006), “A Functional Wavelet- Kernel Approach for Time Series Prediction,” Journal of the Royal Statistical Society, Series B, 68, 837–857. DOI: 10.1111/j.1467-9868.2006.00569.x.
   Google Scholar
• Antoniadis, A., Paparoditis, E., and Sapatinas, T. (2009), “Bandwidth Selection for Functional Time Series Prediction,” Statistics & Probability Letters, 79, 733–740.
   Web of Science ®Google Scholar
• Antoniadis, A., and Sapatinas, T. (2003), “Wavelet Methods for Continuous-Time Prediction using Hilbert-valued Autoregressive Processes,” Journal of Multivariate Analysis, 87, 133–158. DOI: 10.1016/S0047-259X(03)00028-9.
   Web of Science ®Google Scholar
• Aue, A., Dubart Norinho, D., and Hörmann, S. (2015), “On the Prediction of Stationary Functional Time Series,” Journal of the American Statistical Association, 110, 378–392. DOI: 10.1080/01621459.2014.909317.
   Web of Science ®Google Scholar
• Baranowski, R., and Piotr, F. (2020), “Multiscale Autoregression on Adaptively Detected Timescales,” http://stats.lse.ac.uk/fryzlewicz/amar/amar.pdf
   Google Scholar
• Besse, P. C., Cardot, H., and Stephenson, D. B. (2000), “Autoregressive Forecasting of Some Functional Climate Variations,” The Scandinavian Journal of Statistics, 27, 673–687. DOI: 10.1111/1467-9469.00215.
   Web of Science ®Google Scholar
• Bosq, D. (2000), Linear Processes in Function Spaces, New York: Springer-Verlag.
   Google Scholar
• Cai, T. T., and Hall, P. (2006), “Prediction in Functional Linear Regression,” The Annals of Statistics, 34, 2159–2179. DOI: 10.1214/009053606000000830.
   Web of Science ®Google Scholar
• Chiou, J.-M. (2012), “Dynamical Functional Prediction and Classification, with Application to Traffic Flow Prediction,” The Annals of Applied Statistics, 6, 1588–1614. DOI: 10.1214/12-AOAS595.
   Web of Science ®Google Scholar
• Chiou, J.-M., and Li, P.-L. (2007), “Functional Clustering and Identifying Substructures of Longitudinal Data,” Journal of Royal Statistical Society, Series B, 69, 679–699. DOI: 10.1111/j.1467-9868.2007.00605.x.
   Google Scholar
• Delaigle, A., Hall, P., and Pham, T. (2019), “Clustering Functional Data into Groups by using Projections,” Journal of the Royal Statistical Society, Series B, 81, 271–304. DOI: 10.1111/rssb.12310.
   Google Scholar
• Didericksen, D., Kokoszka, P., and Zhang, X. (2012), “Empirical Properties of Forecasts With the Functional Autoregressive Model,” Computational Statistics, 27, 285–298. DOI: 10.1007/s00180-011-0256-2.
   Web of Science ®Google Scholar
• Hall, P., and Horowitz, J. L. (2007), “Methodology and Convergence Rates for Functional Linear Regression,” The Annals of Statistics, 35, 70–91. DOI: 10.1214/009053606000000957.
   Web of Science ®Google Scholar
• Hörmann, S., Kokoszka, P. (2010), “Weakly Dependent Functional Data,” The Annals of Statistics, 38, 1845–1884. DOI: 10.1214/09-AOS768.
   Web of Science ®Google Scholar
• Jiao, S., Frostig, R. D., and Ombao, H. (2021), “Filtrated Common Functional Principal Components for Multivariate Functional Data,” arXiv preprint arXiv:2106.01104.
   Google Scholar
• Jiao, S. and Ombao, H. (2019), “Shape-Preserving Prediction for Stationary Functional Time Series.” arXiv preprint arXiv:1910.12046.
   Google Scholar
• Kargin, V., and Onatski, A. (2008), “Curve Forecasting by Functional Autoregression,” Journal of Multivariate Analysis, 99, 2508–2526. DOI: 10.1016/j.jmva.2008.03.001.
   Web of Science ®Google Scholar
• Kokoszka, P., and Reimherr, M. (2013), “Determining the Order of the Functional Autoregressive Model,” Journal of Time series Analysis, 34, 116–129. DOI: 10.1111/j.1467-9892.2012.00816.x.
   Web of Science ®Google Scholar
• Liu, X., Xiao, H., and Chen, R. (2016), “Convolutional Autoregressive Models for Functional Time Series,” Journal of Econometrics, 194, 263–282. DOI: 10.1016/j.jeconom.2016.05.006.
   Web of Science ®Google Scholar
• Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis (2nd ed.), New York: Springer.
   Google Scholar
• Shang, H. L. (2017), “Functional Time Series Forecasting with Dynamic Updating: An Application to Intraday Particulate Matter Concentration,” Econometrics and Statistics, 1, 184–200. DOI: 10.1016/j.ecosta.2016.08.004.
   Web of Science ®Google Scholar
• Shumway, R. H., and Stoffer, D. S. (2011), Time Series Analysis and Its Application (3rd ed.), New York: Springer.
   Google Scholar
• Wang, J. L., Chiou, J. M., and Müller, H. G. (2016), “Functional Data Analysis,” Annual Review of Statistics and Its Applications, 3, 257–295. DOI: 10.1146/annurev-statistics-041715-033624.
   Web of Science ®Google Scholar
• Yao, F., Müller, H. G., and Wang, J. L. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of American Statistical Association, 100, 577–590. DOI: 10.1198/016214504000001745.
   Web of Science ®Google Scholar
• Yao, S.-N., and Shen, Y.-C. (2017), “Functional Data Analysis of Daily Trajectories in Traffic: Transportation Forecasting in the Real-Time,” in 2017 Computing Conference, 1394–1397. London, UK: IEEE.
   Google Scholar