Singular spectrum analysis basics in R

Using the following R package
 http://cran.r-project.org/web/packages/Rssa/index.html

and my time series as the variable: z.ts

Summary: Singular spectrum analysis for time series
Anatoly Zhigljavsky

Singular Spectrum Analysis a technique of times series analysis and forecasting.
Aim is to decompose the original series into a sum of smaller number of interpretable components such as:
slowly varying trend, oscillatory components and a structureless noise.

based on singular value decomposition (SVD) of a specific matrix constructed upon time series.

SSA is a model-free technique because no assumptions such as parametric model nor stationary type

condition is required.

Basic SSA
X= construct the trajectory matrix (lagged vectors)
this matrix is a Hankel Matrix, all elements along the diagonal are equal

the SVD of matrix XX(transpose) yields a collection of L eigenvalues and eigenVectors.

Basic SSA can be used for smoothing,filtration, noise reduction, extraction of trends of different

resolution, extraction of periodicities in the form of modulated harmonics, gap-filling

One of the requirements of SSA is a continuous time series with no Gaps.





in R statistics
s <- new.ssa(z.ts)

suitable grouping of the elementary time series is required via looking at the eigenplots of the

decomposition

plot(s, type = "series", groups = list(1:4)) #Plot the first 4 reconstructed components
plot(s, type = "values") #Plot the eigenvalues

examine the so-called w-correlation matrix
# Calculate the w-correlation matrix between first 10 series
w <- wcor(s, groups = 1:10)
print(w)
plot(w)

reconstruction of the time-series using the selected grouping
# Reconstruct the series, grouping elementary series 2, 3 and 4, 5.
r <- reconstruct(s, groups = list(1, c(2,3), c(4,5)))
plot(r$F1, col = "black")
lines(r$F1 + r$F2, col = "red")
lines(r$F1 + r$F2 + r$F3, col = "blue")

Summary of steps to get the graph

s <- new.ssa(z.ts) # Perform the decomposition using the default window length
summary(s)        # Show various information about the decomposition
plot(s)           # Show the plot of the eigenvalues
f <- reconstruct(s, groups = list(1, c(2, 3), 4)) # Reconstruct into 3 series
plot(z.ts)         # Plot the original series
lines(f$F1, col = "blue")            # Extract the trend
lines(f$F1+f$F2, col = "red")        # Add the periodicity
lines(f$F1+f$F2+f$F3, col = "green") # Add slow-varying component

Forcast
# Produce 5 forecasted values and confidence bounds of the series using
# the first 3 eigentriples as a base space for the forecast.
bforecast(s, group = 1:3, len = 5)