Diagnosing Non-Mean-Reverting Volatility in GARCH Models
Summary
The document describes an attempt to fit hourly Bitcoin returns with asymmetric GARCH-family models. The reported fit has a portmanteau statistic of 198.4 and an estimated first ARCH and GARCH coefficient sum above one, raising concern about volatility persistence and mean reversion. The user also asks whether seasonality or jumps might need to be represented and notes a software limit on model orders.
The response suggests that removing the lagged conditional-variance term (setting beta to zero) yields an ARCH specification, and explains that estimating larger orders becomes harder as the number of parameters and candidate combinations grows. Its broader recommendation is to investigate the data and diagnose the model’s shortcomings before trying more complex specifications. This is a short discussion rather than a full modeling guide: it does not assess the reported residual diagnostics, establish that ARCH is an appropriate correction, or provide a tested alternative for the Bitcoin series.
Key ideas
- A coefficient sum above one raises questions about volatility persistence and mean reversion in the fitted model.
- Setting the lagged variance coefficient to zero produces an ARCH-style model, according to the response.
- Higher model orders increase the parameter-estimation burden and the number of candidate specifications.
- Model choice should follow diagnosis of issues such as seasonality or jumps rather than indiscriminate order searches.
- The proposed ARCH adjustment is not validated against the Bitcoin data in the discussion.
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# How would you correct a GARCH model to deal with non mean reverting volatility? # 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. ## Answer by Lucas Morin (score 1) https://quant.stackexchange.com/a/11049 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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