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Additionally, augmenting GARCH models with asymmetric power terms to obtain APGARCH models and merging fractional integration with APGARCH models to obtain FIAPGARCH models provide improvements in terms of volatility modeling.
These statistical models provide improvements over the earlier qualitative indices.
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Overall, the MLP- and RBF-based models provide improvement over the GARCH and LSTAR-LST-GARCH two regime variants.
Such models are unlikely to provide improvements to our results while adding substantial complexity to the analysis as well as free parameters whose data-based estimation may result in overfitting.
The negative aspects of adding a second model are of two types: i) those that have to do with a 2D approach, and which are described above, and ii) those that are associated to the fact that not all additional models provide an improvement.
The spatially weighted Tobit models provide a slight improvement in explanatory power compared to the original Tobit.
In one of the cases, optimization over multiple history-matched models provides significant improvement over optimizing with a single model.
Compared to the LSTAR-LST-GARCH models, the models provided significant improvement.
Results supported the following conclusions for modeling and forecasting volatility in crude oil prices: (i) The nonlinear volatility models with STAR type nonlinearity namely, LSTAR-LST-GARCH family provided significant gains in terms of in-sample (one-step-ahead) forecasting accuracy and these models provided significant improvement over their single-regime GARCH variants.
Including either a constant or quadratic term in these models provided no improvement in fit so we have no evidence to contradict the assumed exponential decay model or to suggest that loss was age-dependent (age and interval length are strongly confounded in this study design).
A good criterion would be to set the resolution limit such that the highest resolution data still provide improvement in the model, with somewhat more convincing CC and I/σI statistics.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com