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Hello everyone!

I'm working on a time series regression, which I want to keep linear. I have trouble with serial correlation, there is serious autocorrelation present. I'd like to add an autoregressive term to my equation. According to the partial correlation graph, AR(1) would suit. Additionally, I'm thinking about adding an MA term, possibly then ARMA (1,7).

My question is, can I still use the regressor-coefficients for inference? Their values don't change dramatically. Is my model still linear or what happens when I add the ARMA terms? Sorry for possibly sounding naive, but that confuses me and I'd really like to use the coefficients of my linear model!

Help would be much appreciated! Thanks!

If you add AR and/or MA terms to your linear regression, your are estimating an ARMAX model.

In order to do inference, your residuals should be gaussian white noise (GWN). So,

1) Adding AR and/or MA terms certanly would fix the autocorrelation problems, and maybe you can even get GWN errors to make inference, but
2) You're faced with another, potentially destructive problem: misspecification, if an ARMAX equation is NOT the correct functional form to test your coefficients. (To my knowledge, some simultaneous structural models could in fact be represented as univariate ARMA models, you have to check if it is your situation)

My suggestion is nevertheless to try to understand the origin of the serial correlation problems, rather than just trying to fix it. I mean, maybe if you try with an ADL model or another specification you'll get better results than just fixing the problem in your (static?) equation