Econometric Model Functional Forms

I need some advice in selecting the proper functional form to model the relationship between VIX & a group of S&P500 equities.

What I've read seems to center around GARCH and ARIMA models, neither of which I fully understand.

Does anyone have material or advice on these econometric models? It seems GARCH is used to model future stock returns based off the individual stock's previous values (rather than the values of a separate coefficient).

I am simply building a trading strategy to compliment an undergraduate honours thesis, and I believe the model will draw conclusions to optimize holding period/significance of relative levels of the VIX.

Any advice is much appreciated.

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Econometric Model Functional Forms

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