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- W1964924307 abstract "Abstract In representing random processes, choice of appropriate model structure is generally one of the most important yet difficult considerations. In recent years, models have been developed which expand the possibilities for representing extensive correlation structures, useful for time series which exhibit long memory in the sense that current samples contain information from the distant past. This class of models is based on archetypes which may be defined in terms of Gegenbauer polynomials. Such previous research has used approximation-based determination of Gegenbauer models from data. In this paper, some of the models' properties and associated procedures are developed further. Thus, the exact autocorrelation function is given, which makes it possible to use the exact likelihood for estimating the model parameters and identifying the structure versus simpler alternatives, on the basis of modest sample sizes. Recursion relations are also given for the easy calculation of the autocorrelation function, despite its complicated form. Accuracy of the estimation procedure is demonstrated to be near the Cramer-Rao bound. The identification procedure is also demonstrated to be successful, choosing the correct models in numerical experiments. Comparison with the earlier fractional difference models is also made. Thus, the Gegenbauer models are further established as effective options for representing random processes." @default.
- W1964924307 created "2016-06-24" @default.
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- W1964924307 date "1997-11-01" @default.
- W1964924307 modified "2023-09-25" @default.
- W1964924307 title "Determination of Gegenbauer-type random process models" @default.
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- W1964924307 doi "https://doi.org/10.1016/s0165-1684(97)00142-4" @default.
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