I have trained a GARCH(1,1) model that does a decent job of forecasting volatility (for real-world stock price time-series). For "known" events such as earnings announcements one can ignore historical jumps for a base forecast and add back some estimate of future jumps on these events. But how can I model "unknown" events or jumps? My gut says I need to model some kind of poisson process.
I don't have any formal education in quantitative finance, so I'm looking for ideas/references/pointers or even terminology that I can use to explore solutions. The end goal is practical application in volatility forecasting of equities.
So far I've discovered Jump-diffusion and SVJ, both of which I suspect are not great for forecasting. I also discovered jump-GARCH and poisson-GARCH and these look more promising. Are there any other options?
