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I recently studied and implemented the intraday periodicity model of Andersen and Bollerslev from here.

https://www.sciencedirect.com/science/article/abs/pii/S0927539897000042

The seasonality captured by the model on an equity index looks fine on the 5 minute timescale.enter image description here

Can anyone validate this result and explain the next step in the process for modelling returns and volatility.

Edit : So i fitted Arima models to both un-adjusted and adjusted returns (Rf = R/si) ,but couldn't see any significant improvements in r-squared.

Edit 2 : Have tried a bunch of things (prediction , backtesting ,..). The results do not improve for any model. Could someone point me to the right direction as to what i am doing wrong.

Edit 3: Just tried the weirdest idea i ever had : "Intraday Periodicity adjusted Bollinger Bands". The results weren't great else would have published a paper :).

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