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The concepts of physical dependence and approximability have been extensively used over the past two decades to quantify nonlinear dependence in time series. We show that most stochastic volatility models satisfy both dependence conditions, even if their realizations take values in abstract Hilbert spaces, thus covering univariate, multi‐variate and functional models. Our results can be used to apply to general stochastic volatility models a multitude of inferential procedures established for Bernoulli shifts. 

Abstract. Comparisons of observed and modeled climate behavior often focus on central tendencies, which overlook other important distributional characteristics related to quantiles and variability. We propose two permutation procedures, standard and stratified, for assessing the accuracy of climate models. Both procedures eliminate the need to model cross-correlations in the data, encouraging their application in a variety of contexts. By making only slightly stronger assumptions, the stratified procedure dramatically strengthens the ability to detect a difference in the distribution of observed and climate model data. The proposed procedures allow researchers to identify potential model deficiencies over space and time for a variety of distributional characteristics, providing a more comprehensive assessment of climate model accuracy, which will hopefully lead to further model refinements. The proposed statistical methodology is applied to temperature data generated by the state-of-the-art North American Coordinated Regional Climate Downscaling Experiment (NA-CORDEX).