Analysis of time series structure ssa and related techniques pdf
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Modern Time Series Analysis - SciPy 2019 Tutorial - Aileen Nielsen
Singular spectrum analysis
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Over the last 15 years, singular spectrum analysis SSA has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing.
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In time series analysis , singular spectrum analysis SSA is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics , multivariate geometry, dynamical systems and signal processing. SSA can be an aid in the decomposition of time series into a sum of components, each having a meaningful interpretation. The name "singular spectrum analysis" relates to the spectrum of eigenvalues in a singular value decomposition of a covariance matrix , and not directly to a frequency domain decomposition. The origins of SSA and, more generally, of subspace-based methods for signal processing, go back to the eighteenth century Prony's method. These authors provided an extension and a more robust application of the idea of reconstructing dynamics from a single time series based on the embedding theorem. Several other authors had already applied simple versions of M-SSA to meteorological and ecological data sets Colebrook, ; Barnett and Hasselmann, ; Weare and Nasstrom,