Spectral Analysis of Stationary Processes

2018 ◽  
pp. 531-548
Author(s):  
Frank Beichelt
Keyword(s):  
Spectral Analysis ◽  
Stationary Processes

Random Processes and Fields

1996 ◽  
Author(s):  
Ilya Polyak
Keyword(s):  
Spectral Analysis ◽  
Correlation Analysis ◽  
Random Function ◽  
Numerical Algorithms ◽  
Random Processes ◽  
Multidimensional Case ◽  
Stationary Processes ◽  
Spectral Window ◽  
Estimation Procedures ◽  
Analogous Reasoning

In this chapter, the nonparametric methods of estimating the spectra and correlation functions of stationary processes and homogeneous fields are considered. It is assumed that the principal concepts and definitions of the corresponding theory are known (see Anderson, 1971; Box and Jenkins, 1976; Jenkins and Watts, 1968; Kendall and Stuart, 1967; Loeve, 1960; Parzen, 1966; Yaglom, 1986); therefore, only questions connected with the construction of numerical algorithms are studied. The basic results ranged from univariate process to multidimensional field are presented in Tables 3.1 and 3.2. These formulas make it possible to compare and trace the formal character of developing estimation procedures when the dimensionality is increasing. The schemes in these tables, as well as the formulas in the previous chapters, can be used for software development without any rearrangement. In part, this approach presents the application of the methods of Chapters 1 and 2 in evaluating random function characteristics. Of course, the final identification of the algorithm parameters (for example, the spectral window widths) can be made only through trial and error and by taking into account the character of the problem under study, that is, the physical properties of the processes and fields observed. The last section of this chapter presents results of the application of these methods to the analysis of some climatological fields. Here the basic results of the univariate spectral analysis are briefly discussed in order to develop algorithms for a multidimensional case by analogous reasoning. The complete description of the estimation procedures of the spectral and correlation analysis for univariate stationary process can be found, for example, in Jenkins and Watts, 1968.

ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES

2009 ◽  
Vol 26 (4) ◽  
pp. 1218-1245 ◽  
Author(s):  
Weidong Liu ◽  
Wei Biao Wu
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Spectral Density ◽  
Fundamental Problem ◽  
Classical Problem ◽  
Stationary Processes ◽  
Density Estimates ◽  
Consistency And Asymptotic Normality ◽  
White Noises ◽  
Analysis Of Time Series

We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

CAPABILITY MEASURES FOR m -DEPENDENT STATIONARY PROCESSES

Statistics ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 1-24 ◽  
Author(s):  
SY-MIEN CHEN ◽  
YU-SHENG HSU ◽  
W. L. PEARN
Keyword(s):  
Stationary Processes
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