Let \documentclass[12pt]{minimal}\begin{document}${\sl Aut}_{mHH}(H)$\end{document}AutmHH(H) denote the set of all automorphisms of a monoidal Hopf algebra H with bijective antipode in the sense of Caenepeel and Goyvaerts [“Monoidal Hom-Hopf algebras,” Commun. Algebra 39, 2216–2240 (2011)] and let G be a crossed product group \documentclass[12pt]{minimal}\begin{document}${\sl Aut}_{mHH}(H)\times {\sl Aut}_{mHH}(H)$\end{document}AutmHH(H)×AutmHH(H). The main aim of this paper is to provide new examples of braided T-category in the sense of Turaev [“Crossed group-categories,” Arabian J. Sci. Eng., Sect. C 33(2C), 483–503 (2008)]. For this purpose, we first introduce a class of new categories \documentclass[12pt]{minimal}\begin{document}$_{H}\mathcal {MHYD}^{H}(A, B)$\end{document}MHYDHH(A,B) of (A, B)-Yetter-Drinfeld Hom-modules with \documentclass[12pt]{minimal}\begin{document}$A , B \in {\sl Aut}_{mHH}(H)$\end{document}A,B∈AutmHH(H). Then we construct a category \documentclass[12pt]{minimal}\begin{document}${\cal MHYD}(H) =\lbrace {}_{H}\mathcal {MHYD}^{H}(A, B)\rbrace _{(A , B )\in G}$\end{document}MHYD(H)={MHYDHH(A,B)}(A,B)∈G and show that such category forms a new braided T-category, generalizing the main constructions by Panaite and Staic [“Generalized (anti) Yetter-Drinfel'd modules as components of a braided T-category,” Isr. J. Math. 158, 349–366 (2007)]. Finally, we compute an explicit new example of such braided T-categories.

The main aim of this paper is to provide new examples of braided T-categories in the sense of Turaev [Arabian J. Sci. Eng., Sect. C 33(2C), 483–503 (2008)]. For this purpose, we first introduce a class of new twisted Yetter-Drinfeld modules categories. Then, we construct a new braided T-category, generalizing the main constructions by Panaite and Staic [Isr. J. Math. 158, 349–366 (2007)]. Finally, we show that the new braided T-category in some conditions coincides with the representations of a certain Hom-Hopf group-coalgebra that we construct.

The aim of this paper is to construct a new braided T -category via the generalized Yetter-Drinfel'd modules and Drinfel'd codouble over Hopf algebra, an approach different from that proposed by Panaite and Staic [13]. Moreover, in the case of finite dimensional, we will show that this category coincides with the corepresentation of a certain coquasitriangular Turaev group algebra that we construct. Finally we apply our theory to the case of group algebra.

We extend the heterogeneous autoregressive- (HAR-) type models by explicitly considering the time variation of coefficients in a Bayesian framework and comprehensively comparing the performances of these time-varying coefficient models and constant coefficient models in forecasting the volatility of the Shanghai Stock Exchange Composite Index (SSEC). The empirical results suggest that time-varying coefficient models do generate more accurate out-of-sample forecasts than the corresponding constant coefficient models. By capturing and studying the time series of time-varying coefficients of the predictors, we find that the coefficients (predictive ability) of heterogeneous volatilities are negatively correlated and the leverage effect is not significant or inverse during certain periods. Portfolio exercises also demonstrate the superiority of time-varying coefficient models.

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