I am new to regression analysis. Let's say initially I have a linear regression
x = alag(x1) + blag(x2) + clag(x3) -- eq 1
I want to predict the price x based on the the price of x from previous days.
Let's say I believe that lagged volatility y and lagged range (high - low) z also would affect today's price, how could I regress the data? Do I simply do
x = alag(x1) + blag(x2) + clag(x3) + dlag(y1) + elag(y2) + flag(y3) + glag(z1) + hlag(z2) + ilag(z3) -- eq 2
Intuitively, I think that the combination of the three factors together for a particular day is useful for the prediction. For example,
x = alag(All factors lag 1) + blag(All factors lag 2) + clag(All factors lag 3) --eq 3
However, by using eq2, it seems like I am treating all factors independently irregardless the data point is from the same day or not. So is there a method to handle the lagged data in groups or I am getting it wrong by thinking that way?