Assume that stock price of a given stock has its own distribution F(X). The industry (sector) of the stock is distributed G(X). The stock market where the stock is traded is distributed H(X). All three arrays are correlated.
What is the effective method of forecasting stock price X?
Depends on what the forecast is based on. If x, y,z represent stock price, sector index value and stock index value, are you trying to find prob (x|y,z), i.e. forecast stock price given numerical values of indices? If so - you can calibrate a tri-variate copula from the time series data of the three variables, and sample the necessary conditional distribution from it. My understanding of the problem might be incomplete, however, from the problem statement above.
@Paresh, Thank You. I will look into copula-based tools.
I am seeking means on how to do forecasting model for stock price, if distribution tests show that the distribution for stock, sector and market are not the same. In case where the individual stock and sector are the same type of distribution, but both differ from the market: how would you approach it?
Assume we separate groups with extreme prices out into a separate group, and verify its tail index to obtain distribution type and found:
Stock = Frechet
Sector = Weibull
Market = Normal (possibly due to effect of large number)
When we talk of 'forecasting', we are forecasting an unknown (value or a distribution) based on a set of known values. If stock, sector, market (unconditional) distributions are known, exactly what are the measurements for forecasting 'future' stock price? If it is based on 'present' stock price, sector index, market index, we need to know something about the market dynamics as well (how 'present' maps into 'future'). Again - this is simply me trying to clarify the question itself.