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Dependence measures for model selection in singular spectrum analysis. (English) Zbl 1455.94058
Summary: Selection of optimal dimension of trajectory matrix in singular spectrum analysis plays an important role in signal reconstruction from noisy time series. A noisy time series is embedded into a Hankel matrix and the dimension of this matrix depends on the window length considered for a time series. The window length requirement of a time series depends on its underlying data generating mechanism. Since the number of columns in a Hankel structured trajectory matrix is a function of number of rows (window length), dimension dependency occurs naturally in the trajectory matrix and this dependency is characterized by the statistical properties of a time series. In this paper, we develop an entropy based dimension dependency measure that accounts for changes in information content in the matrix in response to changes in window length for a time series. We examine the performance of this measure by using simulation experiments and analyzing real data sets. Results obtained from simulation experiments show that the dimension dependency measure finds reasonably meaningful dimension of the trajectory matrix and provides better forecasting outcome when applied to some popular climatic time series and production indices.
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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[1] Marques, C. A.F.; Ferreira, J. A.; Rocha, A.; Castanheira, J. M.; Melo-Gonçalves, P.; Vaz, N.; Dias, J. M., Singular spectrum analysis and forecasting of hydrological time series, Phys. Chem. Earth, 31, 18, 1172-1179, (2006)
[2] Alonso, F. J.; Castillo, J. M.; Pintado, P., Application of singular spectrum analysis to the smoothing of raw kinematic signals, J. Biomech., 38, 5, 1085-1092, (2005)
[3] Yang, B.; Dong, Y.; Yu, C.; Hou, Z., Singular spectrum analysis window length selection in processing capacitive captured biopotential signals, IEEE Sens. J., 16, 19, 7183-7193, (2016)
[4] Colonna, J. G.; Nakamura, E. F., Unsupervised selection of the singular spectrum components based on information theory for bioacoustic signal filtering, Digit. Signal Process., 82, 64-79, (2018)
[5] de Oliveira, M. A.; Vieira Filho, J.; Lopes Jr, V.; Inman, D. J., A new approach for structural damage detection exploring the singular spectrum analysis, J. Intell. Mater. Syst. Struct., 28, 9, 1160-1174, (2017)
[6] Hassani, H.; Soofi, A.; Zhigljavsky, A. A., Predicting daily exchange rate with singular spectrum analysis, Nonlinear Anal.: Real World Appl., 11, 3, 2023-2034, (2010) · Zbl 1188.62297
[7] Soofi, A.; Cao, L., Modelling and Forecasting Financial Data: Techniques of Nonlinear Dynamics, (2002), Kluwer Academic Publishers
[8] Broomhead, D.; King, G., Extracting qualitative dynamics from experimental data, Phys. D: Nonlinear Phenom., 20, 217-236, (1986) · Zbl 0603.58040
[9] Wang, R.; Ma, H.-G.; Liu, G.-Q.; Zuo, D.-G., Selection of window length for singular spectrum analysis, J. Frankl. Inst., 352, 4, 1541-1560, (2015) · Zbl 1395.93373
[10] Viljoen, H.; Nel, D. G., Common singular spectrum analysis of several time series, J. Stat. Plan. Inference, 140, 260-267, (2010) · Zbl 1353.62104
[11] Golyandina, N.; Nekrutkin, V.; Zhigljavski, A., Analysis of Time Series Structure: SSA and Related Techniques, (2001), CRC Press · Zbl 0978.62073
[12] Alharbi, N.; Hassani, H., A new approach for selecting the number of the eigenvalues in singular spectrum analysis, J. Frankl. Inst., 353, 1, 1-16, (2016) · Zbl 1395.94081
[13] Tzagkarakis, G.; Papadopouli, M.; Tsakalides, P., Trend forecasting based on singular spectrum analysis of traffic workload in a large-scale wireless LAN, Perform. Eval., 66, 3-5, 173-190, (2009)
[14] Khan, M. A.R.; Poskitt, D. S., Moment tests for window length selection in singular spectrum analysis of short-and long-memory processes, J. Time Ser. Anal., 34, 2, 141-155, (2013) · Zbl 1273.62200
[15] M.A.R. Khan, D. Poskitt, Description Length Based Signal Detection in Singular Spectrum Analysis, Monash Econometrics and Business Statistics Working Papers 13/10) (2010).
[16] Hall, P.; Vial, C., Assessing the finite dimensionality of functional data, J. R. Stat. Soc. Ser. B, 68, 4, 689-705, (2006) · Zbl 1110.62085
[17] Poskitt, D.; Sengarapillai, A., Description length and dimensionality reduction in functional data analysis, Comput. Stat. Data Anal., 58, 98-113, (2013) · Zbl 1365.62225
[18] Khan, M. A.R.; Poskitt, D. S., A note on window length selection in singular spectrum analysis, Aust. N. Z. J. Stat., 55, 2, 87-108, (2013) · Zbl 1337.62288
[19] Rao, M. M., Harmonizable Cramer and Karhunen Classes of Processes, 5, 279310, (1985), North-Holland.: North-Holland. Amsterdam
[20] Peña, D.; van der Linde, A., Dimensionless measures of variability and dependence for multivariate continuous distributions, Commun. Stat.: Theory Methods, 36, 10, 1845-1854, (2007) · Zbl 1315.62055
[21] Anderson, T. W., Asymptotic theory for principal component analysis, Ann. Math. Stat., 34, 1, 122-148, (1963) · Zbl 0202.49504
[22] Chu, M. T.; Lin, M. M.; Wang, L., A study of singular spectrum analysis with global optimization techniques, J. Global Optim., 60, 3, 551-574, (2014) · Zbl 1310.90089
[23] Harris, T.; Yuan, H., Filtering and frequency interpretations of singular spectrum analysis, Phys. D: Nonlinear Phenom., 239, 20-22, 1958-1967, (2010) · Zbl 1198.94045
[24] Ombao, H. C.; Raz, J. A.; von Sachs, R.; Malow, B. A., Automatic statistical analysis of bivariate nonstationary time series, J. Am. Stat. Assoc., 96, 454, 543-560, (2001) · Zbl 1018.62080
[25] Aue, A.; Horváth, L., Structural breaks in time series, J. Time Ser. Anal., 34, 1, 1-16, (2013) · Zbl 1274.62553
[26] Hyndman, R. J.; Khandakar, Y., Automatic time series forecasting: the forecast package for R, J. Stat. Softw., 27, 3, 1-22, (2008)
[27] Hassani, H.; Heravi, S.; Brown, G.; Ayoubkhani, D., Forecasting before, during, and after recession with singular spectrum analysis, J. Appl. Stat., 40, 10, 2290-2302, (2013)
[28] Hassani, H.; Soofi, A. S.; Zhigljavsky, A., Predicting inflation dynamics with singular spectrum analysis, J. R. Stat. Soc.: Ser. A, 176, 3, 743-760, (2013)
[29] Silva, E. S.; Hassani, H.; Heravi, S., Modeling european industrial production with multivariate singular spectrum analysis: a cross-industry analysis, J. Forecast., 37, 3, 371-384, (2018)
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