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Wavelet methods for time series analysis by Andrew T. Walden, Donald B. Percival

Wavelet methods for time series analysis Andrew T. Walden, Donald B. Percival ebook
Publisher: Cambridge University Press
Page: 611
ISBN: 0521685087, 9780521685085
Format: djvu

An ideal method would allow different window sizes depending on the scales that one is interested in. This method advances Fourier analysis, where the basic shortcoming was that the Fourier spectrum contained only globally average information. Time series analysis covers methods attempting to understand context of series or to make forecasts. Frequency analysis and decompositions (Fourier-/Cosine-/Wavelet transformation) for example for forecasting or decomposition of time series; Machine learning and data mining, for example k-means clustering, decision trees, classification, feature selection; Multivariate analysis, correlation; Projections, prediction, future prospects; Statistical tests (for But in order to derive ideas and guidance for future decisions, higher sophisticated methods are required than just sum/group by. Methods for time series analyses may be divided into two classes: frequency-domain methods and time-domain methods. Spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, stochastic volatility, wavelets and Markov chain Monte Carlo integration methods. Time Series Analysis and Its Applications presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Dyadic wavelet methods, notably including use of the Haar basis, are of interest as an orthogonal decomposition [25,26], however these can only be applicable to exponential period scales, e.g. In general, exploratory period estimation methods suffer from the developed for short microarray time series, Ptitsyn et al. In this way, any sudden event in a time series can be determined to reasonable accuracy through the wavelet method, regardless of any particular frequency that may be associated with the phenomenon. [32] count the number of permutations (with period-p deliberately avoided) whose periodogram peak at p is larger than that of the time series under test . Wavelet analysis techniques, while not as commonly understood as Fourier analysis, are nonetheless frequently applied to problems in which time and frequency information are desired simultaneously.