what it means is that there is no strong evidence against a model with a zero value of the intercept
unless you have a priori reasons to want a non zero intercept, you might be better off with a model with a zero intercept ; at least, i would try this model and compare its performance with the model with a non-zero intercept (in terms of R2 for instance)
How do you suggest I get a model with a zero intercept? just for completeness I am using a model with gaussan distibution but log+1 transformed data nad AR1 autocorrelation structure... in case some of this makes a change
sorry, i had not noticed you were comparing two models
one of your models has a non significant intercept ; this is not such a big deal as long as you do not use this (not significant) value to draw conclusions
(for instance, imagine that your first model has a **significant** value V for the intercept and your second model also has value V for the intercept but **not significant** : you cannot conclude that both models lead to the same value of the intercept !)
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now imagine one of your models had a non significant coefficient for some covariate ; you would try to run another model without this covariate wouldn't you ?
(of course ignoring that non significant coefficient can also result from other reasons than useless covariates ...)
this is the same for the intercept ; so when you have a non significant intercept, you might train another model without intercept just to see what happens ; "morally", this should allow a better estimation of the other significant coefficients
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apologies if all the above handwaving brings more confusion than clarity ...