Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

References

• Aeberhard, W., E. Cantoni, G. Marra, and R. Radice (2021). Robust fitting for generalized additive models for location, scale and shape. Statistics and Computing 31, 11.
   Google Scholar
• Alqallaf, F., S. Van Aelst, V. J. Yohai, and R. H. Zamar (2009). Propagation of outliers in multivariate data. The Annals of Statistics 37, 311–331.
   Google Scholar
• Andrews, D. F., P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers, and J. W. Tukey (1972). Robust Estimates of Location: Survey and Advances. Princeton University Press.
   Google Scholar
• Blázquez-García, A., A. Conde, U. Mori, and J. A. Lozano (2021). A review on outlier/anomaly detection in time series data. ACM Computing Surveys (CSUR) 54 (3), 1–33.
   Google Scholar
• British Standards Institution (2006). BS-EN 14750: Railway applications – Air conditioning for urban and suburban rolling stock. Part 1: Comfort parameters.
   Google Scholar
• Broomhead, D. and G. King (1986). On the qualitative analysis of experimental dynamical systems. In S. Sarkar (Ed.), Nonlinear Phenomena and Chaos, pp. 113–144. Hilger Ltd.
   Google Scholar
• Candès, E. J., X. Li, Y. Ma, and J. Wright (2011). Robust principal component analysis? Journal of the ACM 58 (3), 1–37.
   Google Scholar
• Chang, I., G. C. Tiao, and C. Chen (1988). Estimation of time series parameters in the presence of outliers. Technometrics 30 (2), 193–204.
   Google Scholar
• Chen, K. and M. D. Sacchi (2015). Robust reduced-rank filtering for erratic seismic noise attenuation. Geophysics 80 (1), V1–V11.
   Google Scholar
• Cheng, J., K. Chen, and M. D. Sacchi (2015). Application of Robust Principal Component analysis (RPCA) to suppress erratic noise in seismic records. In SEG Technical Program Expanded Abstracts 2015, pp. 4646–4651. Society of Exploration Geophysicists.
   Google Scholar
• Croux, C., P. Filzmoser, G. Pison, and P. J. Rousseeuw (2003). Fitting multiplicative models by robust alternating regressions. Statistics and Computing 13, 23–36.
   Google Scholar
• Danilov, D. (1997). Principal components in time series forecast. Journal of Computational and Graphical Statistics 6 (1), 112–121.
   Google Scholar
• De Carvalho, M., P. C. Rodrigues, and A. Rua (2012). Tracking the US business cycle with a singular spectrum analysis. Economics Letters 114 (1), 32–35.
   Google Scholar
• De Klerk, J. (2015). Time series outlier detection using the trajectory matrix in singular spectrum analysis with outlier maps and ROBPCA. South African Statistical Journal 49, 61–76.
   Google Scholar
• De la Torre, F. and M. J. Black (2003). A framework for robust subspace learning. International Journal of Computer Vision 54, 117–142.
   Google Scholar
• De Menezes, D., D. M. Prata, A. R. Secchi, and J. C. Pinto (2021). A review on robust M-estimators for regression analysis. Computers & Chemical Engineering 147, 107254.
   Google Scholar
• Fox, A. J. (1972). Outliers in time series. Journal of the Royal Statistical Society Series B: Statistical Methodology 34 (3), 350–363.
   Google Scholar
• Gabriel, K. R. (1978). Least squares approximation of matrices by additive and multiplicative models. Journal of the Royal Statistical Society: Series B (Methodological) 40 (2), 186–196.
   Google Scholar
• Golyandina, N., A. Korobeynikov, and A. Zhigljavsky (2018). Singular Spectrum Analysis with R. Springer.
   Google Scholar
• Golyandina, N., V. Nekrutkin, and A. Zhigljavsky (2001). Analysis of time series structure: SSA and related techniques. CRC press.
   Google Scholar
• Golyandina, N. and A. Zhigljavsky (2020). Singular Spectrum Analysis for Time Series. Springer Berlin, Heidelberg.
   Google Scholar
• Hassani, H., S. Heravi, and A. Zhigljavsky (2009). Forecasting European industrial production with singular spectrum analysis. International Journal of Forecasting 25 (1), 103–118.
   Google Scholar
• Hassani, H. and R. Mahmoudvand (2013). Multivariate singular spectrum analysis: A general view and new vector forecasting approach. International Journal of Energy and Statistics 1 (01), 55–83.
   Google Scholar
• Homod, R. Z. (2013). Review on the HVAC system modeling types and the shortcomings of their application. Journal of Energy 2013, 1–10.
   Google Scholar
• Huang, W. (2023). A two-step singular spectrum analysis method for robust low-rank approximation of seismic data. Geophysics 88 (1), V9–V19.
   Google Scholar
• Hubert, M., P. J. Rousseeuw, and W. Van den Bossche (2019). MacroPCA: an all-in-one PCA method allowing for missing values as well as cellwise and rowwise outliers. Technometrics 61 (4), 459–473.
   Google Scholar
• Hubert, M., P. J. Rousseeuw, and K. Vanden Branden (2005). ROBPCA: a new approach to robust principal component analysis. Technometrics 47, 64–79.
   Google Scholar
• Kallas, S. (2011). White Paper on transport: Roadmap to a single European transport area: towards a competitive and resource-efficient transport system. Office for Official Publications of the European Communities.
   Google Scholar
• Kazemi, M. and P. C. Rodrigues (2023). Robust singular spectrum analysis: comparison between classical and robust approaches for model fit and forecasting. Computational Statistics 38, 1–33.
   Google Scholar
• Lepore, A., B. Palumbo, and G. Sposito (2022). Neural network based control charting for multiple stream processes with an application to HVAC systems in passenger railway vehicles. Applied Stochastic Models in Business and Industry 38 (5), 862–883.
   Google Scholar
• Mahmoudvand, R., F. Alehosseini, and P. C. Rodrigues (2015). Forecasting mortality rate by singular spectrum analysis. RevStat-Statistical Journal 13 (3), 193–206.
   Google Scholar
• Mahmoudvand, R. and P. C. Rodrigues (2016). Missing value imputation in time series using singular spectrum analysis. International Journal of Energy and Statistics 4 (01), 1650005.
   Google Scholar
• Mao, X. and P. Shang (2019). Multivariate singular spectrum analysis for traffic time series. Physica A: Statistical Mechanics and its Applications 526, 121063.
   Google Scholar
• Markovsky, I. (2008). Structured low-rank approximation and its applications. Automatica 44, 891–909.
   Google Scholar
• Maronna, R. A., R. D. Martin, V. J. Yohai, and M. Salibián-Barrera (2019). Robust Statistics: Theory and Methods (with R). John Wiley & Sons.
   Google Scholar
• Maronna, R. A. and V. J. Yohai (2008). Robust low-rank approximation of data matrices with elementwise contamination. Technometrics 50 (3), 295–304.
   Google Scholar
• Muler, N. and V. Yohai (2013). Robust estimation for vector autoregressive models. Computational Statistics & Data Analysis 65, 68–79.
   Google Scholar
• Peña, D. and V. J. Yohai (2023). A review of outlier detection and robust estimation methods for high dimensional time series data. Econometrics and Statistics (in press), 1–19.
   Google Scholar
• Radojicic, U., K. Nordhausen, and S. Taskinen (2023). Singular spectrum analysis. In B. Daya Sagar, Q. Cheng, J. McKinley, and F. Agterberg (Eds.), Encyclopedia of Mathematical Geosciences, pp. 1328–1332. Springer.
   Google Scholar
• Raymaekers, J. and P. J. Rousseeuw (2021). Fast robust correlation for high-dimensional data. Technometrics 63, 184–198.
   Google Scholar
• Raymaekers, J. and P. J. Rousseeuw (2024). Challenges of cellwise outliers. Econometrics and Statistics , appeared online, DOI: 10.1016/j.ecosta.2024.02.002.
   Google Scholar
• Rodrigues, P. C., V. Lourenço, and R. Mahmoudvand (2018). A robust approach to singular spectrum analysis. Quality And Reliability Engineering International 34 (7), 1437–1447.
   Google Scholar
• Rodrigues, P. C. and R. Mahmoudvand (2018). The benefits of multivariate singular spectrum analysis over the univariate version. Journal of the Franklin Institute 355 (1), 544–564.
   Google Scholar
• Rodrigues, P. C., J. Pimentel, P. Messala, and M. Kazemi (2020). The decomposition and forecasting of mutual investment funds using singular spectrum analysis. Entropy 22 (1), 83.
   Google Scholar
• Rousseeuw, P., D. Perrotta, M. Riani, and M. Hubert (2019). Robust monitoring of time series with application to fraud detection. Econometrics and Statistics 9, 108–121.
   Google Scholar
• Rousseeuw, P. J. and A. Leroy (1986). Robust Regression and Outlier Detection. Wiley.
   Google Scholar
• Rousseeuw, P. J. and W. Van den Bossche (2018). Detecting deviating data cells. Technometrics 60 (2), 135–145.
   Google Scholar
• Silva, E. S., Z. Ghodsi, M. Ghodsi, S. Heravi, and H. Hassani (2017). Cross country relations in European tourist arrivals. Annals of Tourism Research 63, 151–168.
   Google Scholar
• Silva, E. S., H. Hassani, M. Ghodsi, and Z. Ghodsi (2019). Forecasting with auxiliary information in forecasts using multivariate singular spectrum analysis. Information Sciences 479, 214–230.
   Google Scholar
• Trindade, A. (2015). Electricity Load Diagrams 20112014. UCI Machine Learning Repository. DOI: 10.24432/C58C86.
   Google Scholar
• Tsay, R. S. (2013). Multivariate Time Series Analysis: with R and Financial Applications. John Wiley & Sons.
   Google Scholar
• Tsay, R. S., D. Peña, and A. E. Pankratz (2000). Outliers in multivariate time series. Biometrika 87, 789–804.
   Google Scholar
• Ye, X., H. Lu, D. Li, B. Sun, and Y. Liu (2004). Thermal comfort and air quality in passenger rail cars. International Journal of Ventilation 3 (2), 183–192.
   Google Scholar
• Zhang, L., H. Shen, and J. Z. Huang (2013). Robust regularized singular value decomposition with application to mortality data. The Annals of Applied Statistics 7, 1540–1561.
   Google Scholar
• Zhu, W. (2022). Robust Singular Spectrum Analysis. In 2022 4th International Academic Exchange Conference on Science and Technology Innovation (IAECST), pp. 1165–1170.
   Google Scholar
• Zhuang, H., H. Wang, and Z. Ji (2022). findPC: An R package to automatically select the number of principal components in single-cell analysis. Bioinformatics 38 (10), 2949–2951.
   Google Scholar