# Regression with Lagged variables

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?

Thanks.

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it really depends on what your assumptions are of independence between the lagged data. – Matt Wolf Apr 6 '13 at 7:22

I think that the combination of the three factors together for a particular day is useful for the prediction.

A shortcut.

Did you formally determine the nature of this combination of the 3 factor together?

Say you come up with the combination: factor1 + factor2 + factor3.

What you can do is considering it as a new variable, eg v to that v = factor1 + factor2 + factor3

You now just have to plug the new variable v into you equation.

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For forecasting and regression methods there is a great, free online textbook by Rob Hyndman. Chapter 9 deals with time-series regression. It is perfectly fine to have correlated factors on the rhs as in your equation 2. The forecast will work but the clear attribution to the regression factors will not possible.

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