4:16 AM (8 hours ago)
Ladies and Gentlemen,
Traditional volatility forecasting has focused on univariate models such as GARCH or its variations which has focused on past values of volatility to predict future values. This approach generally gets one forecast quality that seems to be capped at around 0.4 (considered quite good). For 1-day forecasts of volatility for individual stocks we claim a method that is able to deliver R^2 ~0.65. The main reason we are able to do this is that the aggregate volatility of the entire market has strong predictability (by finance standards) and one can piggyback off this predictability using the aggregate volatility of the entire market as a regression variable.
In the attached png files please find four randomly picked stocks with N=number of days for the forecasting all more than 2000 days. Training period for the model is 500 days rolling. The model is the following:
1. Fit a basic ARFIMA model on aggregate volatility
2. For the individual stock, fit an ARFIMA with aggregate volatility as exogenous variable
3. Predict aggregate volatility and use the prediction to predict the individual stock volatility. The full code is attached which is otherwise self-explanatory.
Also attached are the output for four stocks and the png files containing scatterplots with regression lines. It’s fairly clear that this is going to hold universally for all stocks (for 1-day prediction). This is a fairly significant breakthrough for the issue of volatility forecasting — the attached survey of Poon-Granger shows a survey of results in this field in order to benchmark the achievement of R^2 ~ 0.65 universally.
The full dataset is attached gzipped so that other stocks can be tested.
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