hks


Total Posts: 2 
Joined: Nov 2021 


I observe a mid price at time t0 and have a forecast model that provides mid forecasts (incl. confidence intervals) for time points t1, t2, ... (e.g. 1, 5, ... second look ahead).
How do I best combine the forecasts to produce a sensible mid price at time t0?
The solution appears obvious for the extreme cases (e.g. for perfect forecasts, or no predictive power in the forecasts), but I am unsure how to conceptualise the problem for the practically interesting case when there is some small predictive power, diminishing with the forecast horizon.
Thanks for any thoughts / pointers!




ronin


Total Posts: 708 
Joined: May 2006 


I think there's a typo in there somewhere.
You already have the midprice at t0. It's what generates your forecasts. If you invert the forecast model, you'll get back the original price that you started with.
The way it's written, it doesn't make sense to me. 
"There is a SIX am?"  Arthur 

hks


Total Posts: 2 
Joined: Nov 2021 


thanks, Ronin.
i am conflating mid price at t0 (observable) with an estimate of the "fair value" (latent) at time t0.
consider an example: the observable mid at t0 is 100 and i have a forecast that tells me with certainty that at t1 the mid level will be 110. in this scenario, it's sensible to use 110 as a fair value estimate, i.e. include a skew to the observable mid at t0. even if the 110 is not certain, I'd have a fair value estimate > 100 at t0.
now the question is how to consistently integrate multiple mid forecasts with uncertainty into a fair value estimate at time t0.




ronin


Total Posts: 708 
Joined: May 2006 


Got it.
I don't think you necessarily want to model the mid directly, especially with uncertainty. I would think in terms of "where would I want to buy this" and "where would I want to sell this", maybe with various confidences at various levels. Like, you would 100% buy at the lowest prediction, maybe 80% at the second lowest etc.
Then the mid comes out as what ever it comes out as. And the pure geometric average mid may or may not be the best estimate  some probability weighted average might or might not work better. 
"There is a SIX am?"  Arthur 
