By Harry L. Hurd

Uniquely combining concept, program, and computing, this ebook explores the spectral method of time sequence analysisThe use of periodically correlated (or cyclostationary) techniques has turn into more and more renowned in a number of learn components similar to meteorology, weather, communications, economics, and laptop diagnostics. Periodically Correlated Random Sequences offers the most principles of those techniques by using uncomplicated definitions in addition to motivating, insightful, and illustrative examples. wide assurance of key ideas is supplied, together with second-order idea, Hilbert areas, Fourier conception, and the spectral concept of harmonizable sequences. The authors additionally offer a paradigm for nonparametric time sequence research together with checks for the presence of notebook structures.Features of the e-book include:An emphasis at the hyperlink among the spectral concept of unitary operators and the correlation constitution of workstation sequencesA dialogue of the problems with regards to nonparametric time sequence research for computing device sequences, together with estimation of the suggest, correlation, and spectrumA balanced mix of ancient history with sleek application-specific references to periodically correlated processesAn accompanying website that includes extra routines in addition to facts units and courses written in MATLAB® for acting time sequence research on facts which may have a laptop structurePeriodically Correlated Random Sequences is a perfect textual content on time sequence research for graduate-level facts and engineering scholars who've prior event in second-order stochastic techniques (Hilbert space), vector areas, random techniques, and chance. This e-book additionally serves as a important reference for study statisticians and practitioners in components of likelihood and information corresponding to time sequence research, stochastic tactics, and prediction idea.

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**Extra info for Periodically Correlated Random Sequences: Spectral Theory and Practice (Wiley Series in Probability and Statistics)**

**Sample text**

Huang [130,131] to be of great interest. An extensive body of related work on periodic control [15-171 has a direct relation to PC sequences. For connected work in economics, see the book by P. H. Franses [60] and the references therein. A recent survey on cyclostationarity by Gardner, A. 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.

Sums of periodic and stationary sequences are among the simplest of PC sequences, although it is important to understand them. Perhaps a little more interesting are the cases where additive periodic components are not present. Such are the following cases. 3 If X t is wide sense stationary with E { X t } = 0 and sequence f t = f t + T , then yt = f t xt ft is a scalar periodic ' is P C with period T . 6) 22 EXAMPLES, MODELS, AND SIMULATIONS In engineering, it is sometimes said that Yt is produced by amplitude m o d ulation of a stationary process by a scalar periodic function.

T - 11 and XI, A 2 E [0,27r). If X t is periodically stationary with fourth moments and uniformly &mixing with C,"=-,(&)1/2 < 00 and k ( j ) is any sequence with C,"=-,k ( j ) / ~ ' I l