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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Probabilistic Properties
verfasst von : Jan G. De Gooijer
Erschienen in: Elements of Nonlinear Time Series Analysis and Forecasting
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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.