In the paper we test the efficiency and speedup achieved by parallel computation of the main computational block of a VARMAX-Search algorithm, as compared to the time absorbance of a standard sequential algorithm. The VARMAX-search algorithm is an extension of a fast estimation algorithm, originally presented by Spliid [10]. Whereas the original algorithm assumed that the model orders where known a priori, the present algorithm determines the orders in a cartesian search procedure, where model contenders are estimated at different plausible lag structures and evaluated by standard statistical criteria. Previous evidence suggests that our algorithm tends to favor parsimonious model structures.