Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Form...

We propose parametric tests for serial correlation in levels and squares that exploit the non-normality of financial returns. Our are robust to distributional misspecification. Furthermore, our mean predictability can be robustified against time-varying volatility. Local power analyses confirm their gains over existing methods, while Monte Carlo exercises assess finite sample reliability. apply...