Trispectrum deconvolution of linear processes with randomly missing observations

Abstract

In a large application area of time series analysis ± geophysical exploration ± the underlying innovations sequence is of primary interest and must be estimated. This sequence is estimated by deconvolving the non-Gaussian stationary time series. The deconvolution of a non-Gaussian non-minimum phase linear process, when some observations are missing according to a point binomial distribution is considered. This analysis tools are the bispectrum and the trispectrum. A Monte Carlo study is performed to illustrate the proposed methods.

A bootstrap-based approach for parameter and polyspectral density estimation of a non-minimum phase ARMA process

“…Second and higher order spectral analysis is commonly used for a considerable number of applications in such diverse fields as engineering, economics, sonar and radar technology, biomedicine, seismology, physics (see e.g. Gabr and Al-Ibrahim 2002;Händel 2006;Shin, Mutlu, Koomen, and Markey 2007;Übeyli 2009;Acharya, Chua, Chua, Min, and Tamura 2010;Chua, Chandran, Acharya, and Lim 2010;Gu, Shao, Hu, Naid, and Ball 2011;Mohebbi and Ghassemian 2012, and the references therein). Higher order spectra have an upper hand over spectral analysis in numerous practical situations where one has to analyse the non-Gaussian property of a stochastic process or the nonlinearity of a system operation under random input.…”