I would like to fit the following model
Y (t) = m (t) + b * t + g * C (t) + N (t) with m (t) to be the long term mean monthly values (remove seasonal component), b the trend coefficient, C to be the matrix of explanatory variables, and N (t) the error term being AR (1).
I would like to ask you if this model is the same as the following:
Y (t) - m (t) = b * t + g * C (t) + N (t). Forced to have 0 intercept term, or I should also substract the mean from my regressors also.
Moreover, I would like to know if you can propose how this could be implemented, preferably in Matlab, or secondly in R.
I am not familiar with this kind of models yet, so thanks in advance, all help is very much appreciated.