European stocks finished roughly unchanged on Monday, with better-than-anticipated eurozone data serving as a pillar of support, while Spanish shares charged higher as a 10-month government impasse came to an end. IHS Markit said its manufacturing PMI for the eurozone rose to a 30-month high at 53.3, better than a 52.6 estimate from a FactSet consensus of analysts. The services PMI's nine-month high of 53.5 was ahead of a 52.4 estimate.

U.S. stocks closed lower after drifting between slight gains and losses Monday, finishing October with a loss, as stronger-than-expected consumer spending data underlined the view that the economy is growing at a steady pace, while a drop in oil prices and election uncertainty weighed on the minds of investors.

Asian markets were mixed Tuesday after the release of encouraging purchasing managers index data from China and as the Bank of Japan and Australia's central bank largely held firm on their policies. The official manufacturing PMI rose to 51.2 in October from 50.4 in September, adding to signs that the world's second-largest economy is stabilizing. China's official non-manufacturing purchasing managers index, a measure of activity outside factory gates, edged up to 54.0 in October from 53.7 in September.