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Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

From the previous two chapters we have seen that the richness of nonlinear models is fascinating: they can handle various nonlinear phenomena met in practice. However, before selecting a particular nonlinear model we need tools to fully understand the probabilistic and statistical characteristics of the underlying DGP. For instance, precise information on the stationarity (ergodicity) conditions of a nonlinear DGP is important to circumscribe a model’s parameter space or, at the very least, to verify whether a given set of parameters lies within a permissible parameter space. Conditions for invertibility are of equal interest. Indeed, we would like to check whether present events of a time series are associated with the past in a sensible manner using an NLMA specification. Moreover, verifying (geometric) ergodicity is required for statistical inference.

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De Gooijer, J.G. (2017). Probabilistic Properties. In: Elements of Nonlinear Time Series Analysis and Forecasting. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-43252-6_3

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