Spectral estimation for random processes with stationary increments

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Wei Chen (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Haimeng Zhang

Abstract: In studying a stationary random process on R, the covariance function is commonlyused to characterize the second-order spatial dependency. Through the inversionof Fourier transformation, its corresponding spectral density has been widely usedto describe the periodical components and frequencies. When the process is with stationarydth increments, that is, when the resulting process after undertaken dth orderof di erences is stationary, the notion of structure function is put forward. Throughthe inversion formula, the spectrum can be represented by the structure function.In this dissertation, we rst investigate the properties of the proposed Method ofMoments structure function estimator, through which we obtain the spectral densityfunction estimation of the underlying process. In particular, when the process is intrinsicallystationary, which is also a process is with stationary increments of order 1,we derive the spectral density functions for commonly used variogram models. Furthermore,our proposed estimation method is applied to estimate the spectral densityof power variogram models. All of the above results are supplemented via simulationsand a real data analysis. Our results show that the proposed estimation method performswell in recovering the true spectral density function on various processes withstationary increments we considered.[This abstract has been edited to remove characters that will not display in this system. Please see the PDF for the full abstract.]

Additional Information

Language: English
Date: 2018
Aliasing Effect, Intrinsically Stationary Processes, Power Model, Spectral Estimation, Stationary Increments, Structure Function
Spectral theory (Mathematics)
Estimation theory
Stochastic processes
Stationary processes

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