Why doesn't R's arima transform parameters when optimizing using CSS? According to the manual the arima function in R doesn't transform parameters when optimizing using CSS. Is there a particular (statistical) reason for this?  
 A: Conditional Sums of Squares (CSS) has a static one off solution based on the data that does not do recalculation based on the parameter estimates that due to noise variability could lead to non-stationary estimates http://www.stat.berkeley.edu/~aditya/resources/LectureTHIRTEEN.pdf. On the other hand, Maximum Likelihood (ML) estimation has an iterative process of obtaining partial autocorrelation estimates from the data and initial ARIMA parameter estimates, which then with new partial autocorrelation estimates obtains new ARIMA parameter estimates and so on and so on. Based on a variation of Jones (1980), partial autocorrelation transformation is done on potentially theoretically impossible estimated values to the theoretically constrained domain to assure that non-stationary estimates are not provided. Thus, provided the CSS method, transform.pars is not possible. However, CSS may provide a reasonable initial estimate to speed up calculation of a slower, but stationary, ML estimation process. This is why method = CSS-ML + transform.pars = TRUE is the default method for arima() in R.
