Parametric time series models provide explanatory power and a parsimonious description of stochastic dynamical systems. Yet, there is a risk that misspecification of an underlying stochastic model can lead to misunderstanding of the systems, wrong conclusions, and erroneous forecasting. It is common statistical practice to check whether a parametric model fits a given data set reasonably well. To achieve this, in the Neyman-Pearson framework, we need to specify a class of alternative models. The traditional approach is to use a large family of parametric models under an alternative hypothesis. This is basically a parametric approach for model diagnostics. The implicit assumption is that the large family of parametric models specifies the form of the true underlying dynamics correctly. However, this is not always warranted and leads naturally to a nonparametric alternative hypothesis. It is clear that nonparametric models will reduce the danger of model misspecification.
KeywordsMaximum Likelihood Estimator Null Distribution Nonparametric Model Generalize Likelihood Ratio Test Generalize Likelihood Ratio
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