Regression with Lagged Predictors and Grouped Factors
Summary
The discussion considers whether a regression can use several days of lagged prices, volatility, and trading range to forecast today's price. One proposed specification gives each factor and lag its own coefficient; another combines the factors observed on the same day before assigning coefficients by lag. The response suggests creating a composite predictor when a theoretically motivated combination is useful, then including that variable in the regression.
A second answer notes that correlated predictors can be included together in a time-series regression. Such a model may still produce forecasts, but correlation can make it difficult to interpret each predictor's separate contribution. The exchange offers general modeling guidance rather than a fitted example or empirical evidence. It does not explain how to select lags, construct or validate a composite, address time-series issues such as stationarity, or compare forecast performance, so those choices require further analysis.
Key ideas
- A regression can assign separate coefficients to each factor at each lag.
- A theoretically motivated combination of same-day factors can be represented as a composite predictor.
- Correlated explanatory variables may be used together, though their individual effects can be hard to interpret.
- The discussion gives no empirical comparison of the alternative specifications.
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# Regression with Lagged variables # 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. ## Answer by tagoma (score 1) https://quant.stackexchange.com/a/7683 > 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. ## Answer by Richi Wa (score 1) https://quant.stackexchange.com/a/7693 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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