# Models that can improve FHS (with possible residuals manipulation)

The Filtered Historical Simulation (FHS) is a tough benchmark.

By:

• choosing among the most complicated ARMA-GARCH variants with automatic model and lag selection,
• manipulating standardized residuals even introducing asymmetric Extreme Value Theory treatment of the tails (e.g. Generalized Pareto Distribution fitting and resampling),
• bootstrapping the manipulated residuals, and
• rebuilding simulated returns with all the desired statistical properties

one can generate scenarios under $$\mathbb{P}$$ that are extremely useful for risk management purposes because they keep almost all the relevant features of the underlying process. I say "almost" because there are other effects that could be missing.

Since nowadays someone says that machine/deep learning applied to time series will allow for a tremendous improvement over the classical time series modeling, this question is to ask which models represent a real improvement over FHS for simulation purposes. Perhaps you know other models - not necessarily from the machine learning field - that are better than FHS.

The task is to generate thousands of paths that are as much realistic as possible when it comes to moments higher than the first one, that is, I'm not interested in the drift (first moment) estimation accuracy.

Could stuff like this be a real improvement when dealing with financial time series simulations?