Regression model with no constant term & more

#1
Hi guys,

There are a bunch of things that I'm getting confused about and while I've researched online for resources to get clarification, I'm still not certain about the answers. So hoping to get some assistance from the experts

1.) can we manually select a regression model that has no constant term? e.g. we have a dataset and we get a model with constant term, but that model is found to be not so good for forecasting/prediction. Then another model is produced but with no constant term - is that possible?

2.) if 1 is possible, then what are the implications of having a no constant term model?

3.) if the data is time series, what impact does the drift have on the forecast? i'm trying to understand what drift really is.

e.g. forecasting savings balance for a portfolio of bank customers and forecasting yield on a product offered by the bank, the model produced "has a drift" - what exactly does that mean, what are its implications and how do we rectify this (e.g. having no constant term?)


thank you a ton :D
 

Dragan

Super Moderator
#2
Yes, to part 1 - I know that Minitab will does this. I'm sure that other software packages will also do this e.g. SAS will run a regression without a constant term.

Perhaps the important implication of forcing the regression model to not have a constant term is that it may produce a set of error terms that do not sum to zero. If you force the error terms to sum zero then you have - in simple regression terms - a biased estimate the regression coefficient i.e. the estimate would be b_1=YBar/Xbar.

In terms of protfolio theory, you could run both regressions i.e. with and without a constant and look to see if the constant term is (statistically) significant different from zero. If it is not, then use the model without the constant term. Using the model without the constant term would result with regression weight that has better precision i.e. a confidence interval (CI) that is narrower than the CI associated with model that includes the constant term.
 
#3
Yes, to part 1 - I know that Minitab will does this. I'm sure that other software packages will also do this e.g. SAS will run a regression without a constant term.

Perhaps the important implication of forcing the regression model to not have a constant term is that it may produce a set of error terms that do not sum to zero. If you force the error terms to sum zero then you have - in simple regression terms - a biased estimate the regression coefficient i.e. the estimate would be b_1=YBar/Xbar.

In terms of protfolio theory, you could run both regressions i.e. with and without a constant and look to see if the constant term is (statistically) significant different from zero. If it is not, then use the model without the constant term. Using the model without the constant term would result with regression weight that has better precision i.e. a confidence interval (CI) that is narrower than the CI associated with model that includes the constant term.

thank you Dragan !! Would it then be appropriate to say that since we have no constant term, our dependent variable is essentially being predicted "completely" by the independent variables although acknowledging that since error terms aren't summing to zero, the predictions may not neccessarily be 100% but that is always going to be the case anyway since the model produced is always the best estimator and not the accurate estimator?


Also, would you be able to explain the "drift" - what it really is, what it impacts and why it isn't good? i'm looking at two models one forecating savings balance and another yield charged on a loan product.

What I know about a drift is that it is analyzed keeping all independent variabels constant and then the dependent variable is observed for a trend - hopefully that is correct interpretation
 
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