GEOS 597e
Spatiotemporal Data Analysis Workshop
Prework 7: Singular
spectrum analysis: theory and algorithm
Last updated 10/13/06. To be
completed prior to class session Weds., Oct. 18th.
Introduction:
This week we'll introduce the
concept of singular spectrum analysis, which contains as its main
element EOF analysis of time series.
Reading:
- Ghil et al.,
2002:
Advanced spectral methods for climatic time series.
Rev. Geophys., 40(1), sections 1-2.2 (pp. 3-1 to 3-11). Section 1 is a nice
introduction to the entire topic of the paper, but focus on Section 2.
Reading questions:
- Under what circumstances might singular spectrum analysis be
useful?
- Write down, using matrix formulation the following Equations
- rule-of-thumb for estimating the dimension M of the trajectory
matrix
- Eq. 9: estimation of the covariance of the trajectory matrix
- Eq. 8: eigendecomposition of the covariance of the trajectory
matrix
- Eq. 10: principal components of the time series
- Eq. 11,12: reconstructed components of the time series,
with appropriate normalization factors
- In the example analysis of the Southern Oscillation Index, how
many EOFs are identified? Why are EOFs 1-2 and 3-4 plotted
together? How many reconstructed components would you construct
for this data series? What is the 'dimension' of this data series
(e.g. loosely speaking, how many things are 'going on' in the time
series?)
- What are the primary uncertainties in performing an SSA analysis
(for which we should be on the lookout)?
Products to hand in (keep a
copy for yourself to use in class discussion):
- Answers to the four reading questions listed above.
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