# How would you correct a GARCH model to deal with non mean reverting volatility?

I am currently attempting to model and forecast volatility of bitcoin but have not been able to find a GARCH model that fits the data appropriately. I've used tick data sampled at 1 hour intervals over a 2 year period and converted it into hourly returns. The best model i have been able to produce so far is an asymmetric garch (3,3) model.

The portmanteau stat is 198.4**

alpha(1)+beta(1) 1.02753

I have tried GARCH-M,EGARCH,TGARCH all up to (3,3). For some reason I cannot specify (p,q) to be any higher than 3? What steps can I take to improve the model further?

Would it be beneficial to account for seasonality or jumps similair to todrov (2011) and andersen and bollerslev(2005)?

Note: limited programming knowledge so would prefer to avoid R, output produced by PCGIVE10.

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## 1 Answer

For the question in your title,

The mean reversion of the volatility is due to the Moving Average part of the volatility process. The solution would be to set $\beta = 0$. In other words you have to use an AR process for the volatility (so an ARCH model for price).

The restriction in p and q come from the estimation process of the parameters. You test different combinations of parameters to find the most likely. By augmenting the number of parameter you will have more combinations to test and the overall likelihood of good candidates will also grow. So the difficulty to estimate parameters is growing very fast with p and q.

My experience in finding adapted models is that you can't test every models and find one of them wich works. You have to study data. You won't be able to improve the model without understanding wath is wrong with your model (lack of seasonality/mean reversion/jump etc ?).

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