By Harry L. Hurd
ISBN-10: 0470182822
ISBN-13: 9780470182826
ISBN-10: 047134771X
ISBN-13: 9780471347712
Uniquely combining concept, program, and computing, this e-book explores the spectral method of time sequence analysisThe use of periodically correlated (or cyclostationary) strategies has turn into more and more renowned in quite a number examine components equivalent to meteorology, weather, communications, economics, and laptop diagnostics. Periodically Correlated Random Sequences offers the most principles of those strategies by using easy definitions in addition to motivating, insightful, and illustrative examples. broad insurance of key suggestions is equipped, together with second-order thought, Hilbert areas, Fourier thought, and the spectral concept of harmonizable sequences. The authors additionally supply a paradigm for nonparametric time sequence research together with checks for the presence of workstation structures.Features of the publication include:An emphasis at the hyperlink among the spectral conception of unitary operators and the correlation constitution of workstation sequencesA dialogue of the problems in relation to nonparametric time sequence research for notebook sequences, together with estimation of the suggest, correlation, and spectrumA balanced mixture of old heritage with smooth application-specific references to periodically correlated processesAn accompanying site that includes extra workouts in addition to info units and courses written in MATLAB® for acting time sequence research on facts which could have a laptop structurePeriodically Correlated Random Sequences is a perfect textual content on time sequence research for graduate-level information and engineering scholars who've earlier event in second-order stochastic procedures (Hilbert space), vector areas, random methods, and likelihood. This ebook additionally serves as a useful reference for study statisticians and practitioners in components of chance and data corresponding to time sequence research, stochastic tactics, and prediction thought.
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Additional resources for Periodically Correlated Random Sequences: Spectral Theory and Practice (Wiley Series in Probability and Statistics)
Sample text
Y,", always permit The answer is no; its success depends on y2having a properly periodic mean, that is, E { K 2 } = R y ( t , t ) must be a proper periodic function. This proper periodicity typically occurs for amplitude modulation models but never occurs for time scale modulation models. 5 (a) Time series of squares y,' for yt = [1+ m c o s ( 2 ~ t / 6 4 ) &, ] with m = 1 (strong modulation). (b) Periodogram of y,", based on one FFT of length 512, with strong peak at index j = 8. 6 Time series.
Much of this appears in the paper by Gardner and Franks [64]. After the initial work by Gladyshev, the topic was seriously examined in the former Soviet Union by Y . A. Dragan and his colleagues; much of their work seems to be summarized in three books [50-521, all in Russian. A. M. Yaglom [227]gives many references and a nice exposition of many of the basic relationships; we recommend this as a reference for those who wish to work in the topic. Much work on cyclostationary processes followed, mainly motivated by communications problems and lead by Gardner, resulting in two books [66,67].
Napolitano, and L. Paura [74] contains a very complete bibliography. During this period of development of PC processes, the theory of harmonizable processes also matured. H. Cram& [36]attributes the word harmonizable to M. L o h e [138],who also wrote about (strongly) harmonizable processes in [139]. Yu A. Rozanov [200] made an important early contribution, before the more recent developments [l,31,38,82,99,100,144,155,169,189]. 1 P C fields indexed on Z2. A collection of second order random variables X,,t indexed on Z2 is called a (strongly) PC field with period ( S .
Periodically Correlated Random Sequences: Spectral Theory and Practice (Wiley Series in Probability and Statistics) by Harry L. Hurd
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