Nonparametric specification analysis of dynamic parametric models
Time series parametric models generally cater to a particular objective, such as forecasting, and it is therefore desirable to judge such models solely on the basis of their performance in the fullfillment of that objective. We propose a specification testing procedure which concentrates power on the parametric model's ability to estimate a set of characteristics of the finite dimensional distributions of the process. It is based on the comparison between a nonparametric estimate of the said characteristic and its parametric boot-strap analogue. Applications of this principle are proposed for the assessment of recursive dynamic models in the estimation of conditional means and conditional quantiles for mixing processes and for the estimation of dependence in long memory processes.
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