I have data from a time series which I am currently fitting with a linear model. For that Im using the data as cross-sectional data, where each response corresponds to the value of each variable on the next time point.
Parameter estimates for different sized models through OLS (and regularized variants) are pretty good. The problem is that Im neglecting the fact that Im using time series data and have thus correlated errors and nonstationarity of the variables. This appears on a residual plot, showing that the errors follow patterns, which makes the calculation of the residual variance and standard errors of estimates very untrustworthy.
So I was looking for a way to incorporate correlated residuals and possibly the problem of moving averages of the variables into the model.
Im not very familiar with ARMA models and its variants. Is there a standard procedure to stay with the linear model and incorporate ARMA to find the coefficients by means of OLS?