Model Checking via Parametric Bootstraps in Time Series Analysis

SUMMARY This paper uses parametric bootstraps in conjunction with selected functionals such as the spectral density function to derive methods for model checking in time series analysis. The methods proposed emphasize the reproducibilities of the fitted models. They are widely applicable and easy to implement. In particular, they can be used to check special characteristics of the underlying process such as time reversibility and long memory dependence. The paper also addresses the importance of model-building objectives in model checking. Several examples including a wind speed data set for Ireland are used to illustrate the procedures proposed.