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If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1) $, then what does this constant term imply? Will it hamper the estimates if the constant term is ignored?

The question is in terms of estimation of linear models using Maximum Likelihood estimation or any other estimation technique, where in most of the examples I have seen that the parameters are estimated and not the constant terms.

Glen_b
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Ria George
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    These answers touche on the issue of the constant term, http://stats.stackexchange.com/questions/111544/removing-the-intercept-term-in-a-dynamic-regression-justified/111571#111571, and http://stats.stackexchange.com/questions/80790/deliberately-fitting-a-model-without-intercept/80798#80798although as @Glen_b notes, time series have their own aspects on the matter (such as differencing, that validly eliminates the constant). – Alecos Papadopoulos Aug 30 '14 at 18:24

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You left out the error term from your model.

Looks like you're fitting an AR(1) model.

If $|a|<1$ then the constant term is a function of the common mean, $E(y)$ and the parameter $a$.

It's equivalent to fitting $(y(t)-\mu) = a(y(t-1)-\mu)+\epsilon_t$

The question is in terms of estimation of linear models using Maximum Likelihood estimation or any other estimation technique, where in most of the examples I have seen that the parameters are estimated and not the constant terms.

The constant term is a parameter.

It sounds like all the cases you have dealt with have mean $E(y)=0$. Time series don't usually do that (though if you've differenced the data first, then it's typical to omit constants).

Glen_b
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  • If I want to omit the constant term, then you mentioned that I need to omit the mean(y). I don't have any database, the time series is generated using deterministic model $x(t+1) = 4x(t)(1-x(t))$ & Then the AR(1) model becomes $y(t+1) = 0.2+ y(t) + x(t)$. So, AR(1) and other higher order models are driven by $x$ which acts as the noise. Then, I apply MLE and Least Squares to estimate the parameters. In order to omit the constant term originally in the model, what should I do?This part is still unclear. How you please elaborate. Thank you – Ria George Aug 31 '14 at 04:18
  • "*If I want to omit the constant term, then you mentioned that I need to omit the mean(y)*" -- no, that's not what I said. Omitting the constant term corresponds to a model where the mean is zero (at least if $|a|<1$). If you're generating data from the deterministic model you mention, AR (or regression more broadly) really isn't appropriate. If you're interested in AR models, don't use the logistic map to generate noise, but if you're interested in modelling that deterministic process, don't use AR for it. Its assumptions aren't satisfied. – Glen_b Aug 31 '14 at 04:33