Intuition in Model Selection

[kszynkar]

Hi,

I was wondering if there are any views on the best way to combine intuition with quantitative model selection for a linear regression model. For example, say you are trying to forecast the log monthly difference of one house price index off another that tends to "lead" it.

One quantitative way of selecting a model would be to try all the different model combinations up to a certain lag and choose the one with the lowest AIC.

However, the issue with this approach is that it can result in coefficients that don't make much sense such (<0 or >1).

Would a good way to approach this to do a constrained regression? My concern is that when you start to use multiple series to forecast one, that you can introduce model biases.

Thanks

[kszynkar]

Perhaps my initial question wasn't clear.

The problem is more if you try to regress two series that should have a link on to each other, such as regressing the monthly log difference in house prices changes on to a few different lags of log differences in mortgage approvals. An increase in mortgage approvals should either lead to more demand for property, and higher prices, so the regression coefficients should be >0. However, if I do a constrained regression, I'm worried about picking up noise in the mortgage approvals series, and artificially making the regression coefficients too high.

Is there a good way of combining the intuition that the coefficients should be >0 with good model selection that won't lead to too high a sensitivity of house prices to mortgage approvals?

Thanks