Singular-spectrum analysis: A toolkit for short, noisy chaotic signals

Vautard, Robert; Yiou, Pascal; Ghil, Michael

doi:10.1016/0167-2789(92)90103-t

Cited by 1,228 publications

(919 citation statements)

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“…to reconstruct contributions from the ST-PCs to each S-PC (Plaut and Vautard, 1994). The reconstructed components (RCs: Ghil and Vautard, 1991;Vautard et al, 1992; were then projected onto their respective S-EOFs to form a time series of maps describing the temperature-index variations captured by each ST-PC in turn. Finally, grid-point series were extracted from these maps, analyzed by MEM, and the resulting spectra summed to form This pattern of LF warming and cooling found by M-SSA is in agreement with general patterns of warming and cooling trends of minimum and maximum temperatures during the last several decades, identified by Karl et al (1993), and with changes in atmospheric circulation patterns over the Western United States indicated by recent changes in high-altitude runoff regimes (Dettinger and Cayan, 1995).…”

Section: Low-frequency (Lf) Variabilitymentioning

confidence: 99%

“…SSA (Colebrook, 1978;Broomhead and King, 1986;Fraedrich, 1986;Vautard and Ghil, 1989;Ghil and Vautard, 1991;Vautard et al, 1992) -a form of temporal PC or EOF analysis -was used for both prefiltering and the long-term analysis of the filtered time series. SSA is a powerful form of PC analysis of the lag-correlation structute of time seiles (Vautard et al, 1992; that is particularly successful in isolating multiple periodic components and trends in short, noisy seiles. SSA has been applied to univariate time series (e.g., Ghil and Mo, 1991a, b;Keppenne and Ghil, 1992;Plaut et al, 1995), to spatially correlated series (Kimoto et al, 1991;Keppene and Ghil, 1993;Plaut and Vautard, 1994), and, in this study, to uncorrelated series.…”

Section: Singular-spectrum Analysis (Ssa)mentioning

confidence: 99%

“…The EOFs in M-SSA contain elements of both spatial and temporal variability and are called space-time EOFs (ST-EOFs: Plaut and Vautard, 1994). The correlation matrix is estimated, cf Equation (2.3) of Vautard et al (1992), so that it has block Toeplitz structure with C x C blocks. This approach imposes symmetry (or antisymmetry) around the mid-lag point upon the resulting ST-EOFs, and in the present application seems to yield 'cleaner' decompositions of the spatio-temporal temperature variability than the non-Toeplitz approach of Broomhead and King (1986).…”

Section: Singular-spectrum Analysis (Ssa)mentioning

confidence: 99%

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Interannual and interdecadal variability in United States surface-air temperatures, 1910-87

1995

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Abstract. Monthly mean surface-air temperatures at 870 sites in the contiguous United States were analyzed for interannual and interdecadal variability over the time interval 1910-87. The temperatures were analyzed spatially by empirical-orthogonal-function analysis and temporally by singularspectrum analysis (SSA). The dominant modes of spatio-temporal variability are trends and nonperiodic variations with time scales longer than 15 years, decadal-scale oscillations with periods of roughly 7 and 10 years, and interannual oscillations of 2.2 and 3.3 years. Together, these modes contribute about 18% of the slower-than-annual United States temperature variance. Two leading components roughly capture the mean hemispheric temperature trend and represent a long-term warming, largest in the southwest, accompanied by cooling of the domain's southeastern quadrant. The extremes of the 2.2-year interannual oscillation characterize temperature differences between the Northeastern and Southwestern States, whereas the 3.3-year cycle is present mostly in the Western States. The 7-to 10-year oscillations are rauch less regular and persistent than the interannual oscillations and characterize temperature differences between the western and interior sectors of the United States. These continental-or regionat-scale temperature variations may be related to climatic variations with similar periodicities, either global or centered in other regions; such variations include quasi-biennial oscillations over the tropical Pacific or North Atlantic and quasi-triennial oscillations of North Pacific sea-surface temperatures.

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Section: Low-frequency (Lf) Variabilitymentioning

confidence: 99%

Section: Singular-spectrum Analysis (Ssa)mentioning

confidence: 99%

Section: Singular-spectrum Analysis (Ssa)mentioning

confidence: 99%

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Interannual and interdecadal variability in United States surface-air temperatures, 1910-87

1995

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“…Our result also suggests that using PCA to pre-filter the data before a factor decomposition is misconceived since both PCA and factor decomposition are one and the same thing. It might however be useful in nonlinear factor decomposition, as suggested from previous nonlinear dynamic studies (Broomhead and King, 1986;Vautard et al, 1992;Chan and Tong, 2001).…”

Section: Self-consistent Calibration Of the Multi-factor Model And Prmentioning

confidence: 99%

Self-consistent asset pricing models

Malevergne

Sornette

2007

Physica A: Statistical Mechanics and its Applications

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We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alpha's and beta's of the factor model are unobservable. Self-consistency leads to renormalized beta's with zero effective alpha's, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value α i at the origin between an asset i's return and the proxy's return. Self-consistency also introduces "orthogonality" and "normality" conditions linking the beta's, alpha's (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from Jan. 1990 to Feb. 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the selfconsistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the self-consistency condition derives a risk-factor decomposition in the multi-factor case which is identical to the principal components analysis (PCA), thus providing a direct link between model-driven and datadriven constructions of risk factors. This correspondence shows that PCA will therefore suffer from the same limitations as the CAPM and its multi-factor generalization, namely lack of out-of-sample explanatory power and predictability. In the multi-period context, the self-consistency conditions force the beta's to be time-dependent with specific constraints.

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“…Possible application areas of SSA are diverse: from mathematics and physics to economics and financial mathematics, from metrology and oceanology to social science and market research (see, for example, [7,8,9,10,11] and references therein). Any seemingly complex series with a potential structure could provide an example of a successful application of SSA [2].…”

Section: Introductionmentioning

confidence: 99%

Singular spectrum analysis based on the minimum variance estimator

Hassani¹

2010

Nonlinear Analysis: Real World Applications

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Abstract-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, we introduce the SSA technique based on the minimum variance estimator. We also consider the SSA technique based on the minimum variance and structured total least squares estimators in reconstructing and forecasting time series. 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.

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Singular-spectrum analysis: A toolkit for short, noisy chaotic signals

Cited by 1,228 publications

References 37 publications

Interannual and interdecadal variability in United States surface-air temperatures, 1910-87

Interannual and interdecadal variability in United States surface-air temperatures, 1910-87

Self-consistent asset pricing models

Singular spectrum analysis based on the minimum variance estimator

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