There will be a Statistics seminar at UMIST on Wednesday 10th November.
Details are given below. All those interested are welcome to attend.
Wednesday 10th November, 3.00pm - 4.30pm
Venue: UMIST, MSS/O10 or possibly MSS/M12 (to be confirmed)
Speaker: Professor Anatoly Zhigljavsky, Cardiff University.
Title: Principal Component Expansions of Time Series: Singular Spectrum
Analysis and Related Technique
Abstract:
SSA, the Singular Spectrum Analysis, is a general term referring to the
technique of time series analysis based on singular value decomposition of
the 'trajectory matrix' formed by combining several lagged copies of a
single series. SSA could be considered as an extension of the Principal
Component Analysis from independent to time-correlated observations.
There is a certain flexibility in the methodology that could make it
extremely powerful. We use a large amount of real data from different fields
to elucidate the key ideas of the methodology, to demonstrate its power, and
to caution about snags.
We also describe some underlying mathematical/statistical models and related
theoretical results. The basic problems here are separation of one signal
from another and separation of a signal from noise. The signals are, roughly
speaking the time series that are well approximated by solutions of
finite-difference equations, and the noise is what could not be well
approximated by solutions of such equations. Noise is thus modelled in a
non-stochastic manner but it could certainly include stochastic components.
The problems we consider are: analysis of structure of time series,
continuation (forecast) of time series, change-point detection. In
developing specific algorithms geometrical ideas and tools are at least as
important as analytical and statistical.
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