Hi,I am working on an autoregression model (with the MATLAB econometrics toolbox by LeSage) and I am wondering the following... Suppose I have a data series, for which I do not know what kind of process it represents, and find statistically significant autocorrelation. I think an average econometrist will subsequently use an AR(x) model to represent the data.. (or ARMA or ARIMA or whatever).However, -> suppose that the data series represents an superposition of an oscillatory pattern and a lot of noise.. then estimating a AR model (or ARMA of ARIMA..) using OLS will result in statistically significant autoregression constants, but would not be the correct way of estimating the process:- Instead of using OLS linear regression of for instance for lag 1: [x_i] with [x_{i-1}], where the formula assumed is: x_i = \alpha x_{i-1} + error_i, we have to consider total least squares (a.k.a. orthogonal regression), where we can estimate: x_i + error_i = \alpha x_{i-1} + error_{i-1}. Using OLS linear regression would result in bias for this data series.I hope I am right so far (?),My question is: how do I know which kind of process I am dealing with? Is there a statistical test for this problem? In addition, what methods can be used for a replacement of a VAR model for the case of the data series described above..THANKS!

Before estimating any AR(1)MA model first remove deterministic part like seasonal pattern, oscillatory pattern etc