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Titlebook: Elements of Nonlinear Time Series Analysis and Forecasting; Jan G. De Gooijer Book 2017 Springer International Publishing Switzerland 2017

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Adrian W. T. Dostal,Gabriele Dostald abandon it only if sufficiently strong evidence for a nonlinear alternative can be found. This approach can be applied using a linearity test, often in combination with a test for Gaussianity. Several test statistics, both in the time domain and frequency domain, have been proposed for this purpose.
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Chancen und Risiken der Kundenintegration when checking the adequacy of a fitted time series model through observed “residuals”, i.e. are they approximately i.i.d. or are there significant deviations from that assumption. In fact, many inference procedures apply only to i.i.d. processes.
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Jonas Schwartze,Klaus-Hendrik Wolfvertibility 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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,DNA von Groß- und Megaprojekten,e (or criterion) helps to identify the most appropriate model for the purpose at hand. Finally, it is common practice to test the series of standardized residuals for white noise via a residual-based diagnostic test statistic.
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Probabilistic Properties,ractice. 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 m
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