A collection of methods for singular spectrum analysis

Description

Singular Spectrum Analysis (SSA, in short) is a modern non-parametric method for the analysis of time series and digital images. This package provides a set of fast and reliable implementations of various routines to perform decomposition, reconstruction and forecasting.

Details

Typically the use of the package starts with the decomposition of the time series using ssa. After this a suitable grouping of the elementary time series is required. This can be done heuristically, for example, via looking at the plots of the decomposition (plot). Alternatively, one can examine the so-called w-correlation matrix (wcor). Next step includes the reconstruction of the time-series using the selected grouping (reconstruct). One ends with frequency estimation (parestimate) and series forecasting (forecast, rforecast, vforecast). In addition, Oblique SSA methods can be used to improve the series separability (iossa, fossa).

References

Golyandina, N., Nekrutkin, V. and Zhigljavsky, A. (2001): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall/CRC. ISBN 1584881941f

Golyandina, N. and Stepanov, D. (2005): SSA-based approaches to analysis and forecast of multidimensional time series. In Proceedings of the 5th St.Petersburg Workshop on Simulation, June 26-July 2, 2005, St. Petersburg State University, St. Petersburg, 293–298. http://www.gistatgroup.com/gus/mssa2.pdf

Golyandina, N. and Usevich, K. (2009): 2D-extensions of singular spectrum analysis: algorithm and elements of theory. In Matrix Methods: Theory, Algorithms, Applications. World Scientific Publishing, 450-474.

Korobeynikov, A. (2010): Computation- and space-efficient implementation of SSA. Statistics and Its Interface, Vol. 3, No. 3, Pp. 257-268

Golyandina, N., Korobeynikov, A. (2012, 2014): Basic Singular Spectrum Analysis and Forecasting with R. Computational Statistics and Data Analysis, Vol. 71, Pp. 934-954. http://arxiv.org/abs/1206.6910

Golyandina, N., Zhigljavsky, A. (2013): Singular Spectrum Analysis for time series. Springer Briefs in Statistics. Springer.

Golyandina, N., Korobeynikov, A., Shlemov, A. and Usevich, K. (2015): Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package. Journal of Statistical Software, Vol. 67, Issue 2. https://www.jstatsoft.org/article/view/v067i02

Shlemov, A. and Golyandina, N. (2014): Shaped extensions of singular spectrum analysis. 21st International Symposium on Mathematical Theory of Networks and Systems, July 7-11, 2014. Groningen, The Netherlands. p.1813-1820. http://arxiv.org/abs/1507.05286

See Also

ssa-input, ssa, decompose, reconstruct, wcor, plot, parestimate, rforecast, vforecast, forecast, iossa, fossa

Examples

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s <- ssa(co2) # Perform the decomposition using the default window length
summary(s)        # Show various information about the decomposition
plot(s)           # Show the plot of the eigenvalues
r <- reconstruct(s, groups = list(Trend = c(1, 4),
                                  Seasonality = c(2:3, 5:6))) # Reconstruct into 2 series
plot(r, add.original = TRUE)  # Plot the reconstruction

# Simultaneous trend extraction using MSSA

s <- ssa(EuStockMarkets, kind = "mssa")
r <- reconstruct(s, groups = list(Trend = c(1,2)))
plot(r, plot.method = "xyplot", add.residuals = FALSE,
     superpose = TRUE, auto.key = list(columns = 2))
# Trend forecast
f <- rforecast(s, groups = list(Trend = c(1, 2)),
               len = 50, only.new = FALSE)
library(lattice)
xyplot(ts.union(Original = EuStockMarkets, "Recurrent Forecast" = f),
       superpose = TRUE, auto.key = list(columns = 2))

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