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Singular spectrum analysis based on the minimum variance estimator. (English) Zbl 1188.62278

Summary: In recent years Singular Spectrum Analysis (SSA), used as a powerful technique in time series analysis, has been developed and applied to many practical problems. In this paper, the SSA technique based on the minimum variance estimator is introduced. The SSA technique based on the minimum variance and least squares estimators in reconstructing and forecasting time series is also considered. A well-known time series data set, namely, monthly accidental deaths in the USA time series, is used in examining the performance of the technique. The results are compared with several classical methods namely, Box-Jenkins SARIMA models, the ARAR algorithm and the Holt-Winter algorithm.

MSC:

62M15 Inference from stochastic processes and spectral analysis
62M20 Inference from stochastic processes and prediction
62H12 Estimation in multivariate analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C60 Computational problems in statistics (MSC2010)
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[1] Soofi, A.; Cao, L., Nonlinear forecasting of noisy financial data, (Soofi; Cao, Modeling and Forecasting Financial Data: Techniques of Nonlinear Dynamics (2002), Kluwer Academic Publishers: Kluwer Academic Publishers Boston)
[2] Tufts, D. W.; Kumaresan, R.; Kirsteins, I., Data adaptive signal estimation by singular value decomposition of a data matrix, Proceedings of the IEEE, 70, 6, 684-685 (1982)
[3] Cadzow, J. A., Signal enhancement a composite property mapping algorithm, IEEE Transactions on Acoustics, Speech, and Signal Processing, 36, 1, 49-62 (1988) · Zbl 0649.93059
[4] Broomhead, D. S.; King, G. P., Extracting qualitative dynamics from experimental data, Physica D, 20, 217-236 (1986) · Zbl 0603.58040
[5] Golyandina, N.; Nekrutkin, V.; Zhigljavsky, A., Analysis of Time Series Structure: SSA and Related Techniques (2001), Chapman & Hall/CRC · Zbl 0978.62073
[6] Vautard, R.; Yiou, P.; Ghil, M., Singular-spectrum analysis: A toolkit for short, noisy chaotic signal, Physica D, 58, 95-126 (1992)
[7] Ghil, M.; Taricco, C., Advanced spectral analysis methods, (Castagnoli, G. C.; Provenzale, A., Past and Present Variability of the Solar-Terrestrial System: Measurement, Data Analysis and Theoretical Model (1997), IOS Press), 137-159
[8] Hassani, H., Singular spectrum analysis: Methodology and comparison, Journal of Data Science, 5, 2, 239-257 (2007)
[9] Hassani, H.; Dionisio, A.; Ghodsi, M., The effect of noise reduction in measuring the linear and nonlinear dependency of financial markets, Nonlinear Analysis: Real World Applications (2009)
[10] H. Hassani, A. Zhigljavsky, Singular spectrum analysis: Methodology and application to economics data, Journal of Systems Science and Complexity (JSSC), (2009) (in press); H. Hassani, A. Zhigljavsky, Singular spectrum analysis: Methodology and application to economics data, Journal of Systems Science and Complexity (JSSC), (2009) (in press)
[11] Hassani, H.; Heravi, H.; Zhigljavsky, A., Forecasting European industrial production with singular spectrum analysis, International Journal of Forecasting, 25, 1, 103-118 (2009)
[12] Moskvina, V. G.; Zhigljavsky, A., An algorithm based on singular spectrum analysis for change-point detection, Communication in Statistics - Simulation and Computation, 32, 2, 319-352 (2003) · Zbl 1075.62625
[13] Golyandina, N.; Osipov, E., Caterpillar-SSA method for analysis of time series with missing values, Journal of Statistical Planning and Inference, 137, 2642-2653 (2006) · Zbl 1121.37065
[14] Ghodsi, M.; Hassani, H.; Sanei, S.; Hicks, Y., The use of noise information for detection of temporomandibular disorder, Journal of Biomedical Signal Processing and Control, 4, 2, 79-85 (2009)
[15] (Danilov, D.; Zhigljavsky, A., Principal Components of Time Series: The Caterpillar Method (1997), University of St. Petersburg Press), (in Russian)
[16] Elsner, J. B.; Tsonis, A. A., Singular Spectrum Analysis. A New Tool in Time Series Analysis (1996), Plenum Press · Zbl 0900.86003
[17] De Moor, B., The singular value decomposition and long and short spaces on noisy matrices, IEEE Transactions on Signal Processing, 41, 9, 2826-2838 (1993) · Zbl 0800.94097
[18] Van Huffel, S., Enhanced resolution based on minimum variance estimation and exponential data modeling, Signal Processing, 33, 3, 333-355 (1993)
[19] Jensen, S. H.; Hansen, P. C.; Hansen, S. D.; Sørensen, J. A., Reduction of broad-band noise in speech by truncated QSVD, IEEE Transactions on Speech and Audio Processing, 6, November, 439-448 (1995) · Zbl 0826.65136
[20] Golub, G.; van Loan, C., Matrix Computations (1996), The Johns Hopkins University Press: The Johns Hopkins University Press London · Zbl 0865.65009
[21] Stewart, G. W.; Sun, J., Matrix Perturbation Theory (1990), Academic: Academic San Diego, CA
[22] Brockwell, P. J.; Davis, R. A., Introduction to Time Series and Forecasting (2002), Springer · Zbl 0994.62085
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