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Higher-order moments, cumulants and spectral densities of the NGINAR(1) process. (English) Zbl 1232.62117

Summary: The motivation for time series with geometric marginal distributions arises from noting that the Poisson distribution is not always suitable for modeling and analysis of integer-valued time series. The NGINAR(1) process that has been introduced by M.M. Ristić et al. [J. Stat. Plann. Inference 139, No. 7, 22318–2226 (2009; Zbl 1160.62083)]) represents a class of such time series. Joint higher-order (factorial) moments and cumulants with some other related statistical measures of the NGINAR(1) process are constructed. Also, the spectral and bispectral density functions of this process are investigated, including their nonparametric estimators, using the multitapering method. A real data example of the nonparametric multitaper spectral estimates is investigated, with a discussion of the results obtained.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
62G05 Nonparametric estimation
62G07 Density estimation
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 1160.62083
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References:

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