@techreport{66449,
  abstract     = {{This paper evaluates the forecasting performance of an expanded class of (semi-)parametric 
GARCH models belonging to the EGARCH family (EGF), including recently introduced long  
and short memory specifications and their semiparametric extensions. The semiparametric 
variants employ a multiplicative volatility decomposition into conditional and slowly varying 
unconditional components, where the latter is estimated via a data-driven local polynomial 
smoother to accommodate non-stationarities commonly observed in financial time series. Based 
on the revised Basel Committee framework for market-risk assessment, all models are capable 
of producing rolling one-day-ahead forecasts for Value at Risk (VaR) and Expected Shortfall 
(ES) under a wide range of symmetric and skewed innovation distributions. Their forecasting 
accuracy is examined using the regulatory traffic light tests for VaR and the recently developed 
ES-specific traffic light procedure, complemented by the regulatory loss function. In addition, 
model selection incorporates both a recently proposed corrected firm-oriented loss function that 
accounts for opportunity costs and the Weighted Absolute Deviation (WAD) criterion. The 
empirical comparison demonstrates that (semiparametric) long memory GARCH models - 
particularly those combining fractional dynamics with nonparametric scale adjustments - can 
serve as valuable alternatives to traditional parametric short memory models, offering more 
stable volatility estimates and improved tail-risk forecasts for practical risk management 
applications.}},
  author       = {{Hanke, Dominik Christian and Uhde, André and Feng, Yuanhua}},
  keywords     = {{semiparametric GARCH extension, data-driven local polynomial smoother, long  memory, GARCH models, Value at Risk, Expected Shortfall, traffic light test, backtesting, Basel  III, market risk}},
  title        = {{{Application of Novel Exponential (Semi-)Parametric Short and Long  Memory GARCH Models under Regulatory Requirements of Basel III}}},
  year         = {{2026}},
}

@article{34814,
  author       = {{Hanusch, Maximilian}},
  issn         = {{0008-414X}},
  journal      = {{Canadian Journal of Mathematics}},
  keywords     = {{extension of differentiable maps}},
  number       = {{1}},
  pages        = {{170--201}},
  publisher    = {{Canadian Mathematical Society}},
  title        = {{{A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}}},
  doi          = {{10.4153/s0008414x21000596}},
  volume       = {{75}},
  year         = {{2023}},
}

@article{34786,
  abstract     = {{A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.}},
  author       = {{Glöckner, Helge and Willis, George A.}},
  issn         = {{0021-8693}},
  journal      = {{Journal of Algebra}},
  keywords     = {{Contraction group, Torsion group, Extension, Cocycle, Section, Equivariant cohomology, Abelian group, Nilpotent group, Isomorphism types}},
  pages        = {{164--214}},
  title        = {{{Decompositions of locally compact contraction groups, series and extensions}}},
  doi          = {{https://doi.org/10.1016/j.jalgebra.2020.11.007}},
  volume       = {{570}},
  year         = {{2021}},
}